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INDEX FOR LOGICAL REASONING

No. Chapter Name Page No.

1 Blood Relations 1.1 Independent Questions

1-5 1.2 Paragraph based questions

1.3 Symbolic Relations based questions 2 Directions and Distances

2.1 Questions to find Distances

2.2 Questions to find Directions 6-8 2.3 Questions to find both Direction and Distance 2.4 Logical Questions based on Directions

3 Coding-Decoding 3.1 Coding with shifting Letters

3.2 Coding with Mathematical Operations 3.3 Coding with Opposite Letters

9-13 3.4 Coding with shuffling Letters

3.5 Coding with random Letters 3.6 Coding with random Numbers

3.7 Coding for corresponding Words 4 Alphabetical Series

4.1 Letter series

4.2 Odd man out 14-16 4.3 Pattern Series 4.4 Letter analogy

5 Number Series 5.1 Gradually Increasing/Decreasing Series

5.2 Drastically Increasing/Decreasing Series 5.3 Alpha-numerical series 17-20 5.4 Alternating Series 5.5 Number Analogy 5.6 Odd man out 6 Set Theory & Venn Diagram

6.1 Introduction to Set theory 21-24

6.2 Table method

6.3 Logical Venn Diagram

7 Syllogisms 25-29

8 Clocks & Calendars

7.1 Questions on clocks 30-32 7.2 Questions on calendars

9 Analytical Ability

8.1 Linear arrangement

8.2 Circular arrangement 33-37 8.3 Tabular arrangement 8.4 Deterministic and Non-deterministic arrangement

10 Data Interpretation

10.1 DI based on Tables

10.2 DI based on Line-graph 38-43 10.3 DI based on Paragraphs(Caselets)

10.4 DI based on Bar-graph 10.5 DI based on Pie-Charts



INDEX FOR QUANTITATIVE SECTION No. Chapter Name Page No.

Number System

1.1 Types of Numbers

1.2 Subtypes of Numbers 1.3 Conversion from Decimal to Fraction 1.4 Divisibility Rules

1 1.5 Rules of Counting Numbers 44-49 1.6 LCM & HCF 1.7 Total number of factors of a natural numbers

1.8 Unit digit of Np

1.9 Finding Remainders when Np is divided by ‗x‘.

1.10 Highest power of prime number in N!

Percentages

2.1 Percent fraction equivalence

2 2.2 Percent change(Increase/ Decrease)

50-54 2.3 Application of Percent Change

2.4 Successive Percent change 2.5 Area of 2-D Figures

Profit, Loss & Discounts

3.1 Basic concept of Cost Price(CP), Selling Price(SP) & Marked Price(MP)

3 3.2 Profit, Loss & Discounts

55-57 3.3 SP of ―x‖=CP of ―y‖

3.4 Dishonest Salesman 3.5 Successive Discount / Profit

Simple & Compound Interest

4 4.1 Simple Interest(SI)

58-59 4.2 Money becomes ―n‖ times

4.3 Compound Interest(CI)

Time and Work

5.1 Working Together

5.2 Work and Wages

5 5.3 Working alternately 60-63 5.4 Pipes & Cisterns 5.5 Working in Groups 5.6 Efficiencies

Time Speed & Distance

6.1 Relation between Time, Speed & Distance

6.2 Conversion from m/s to km/h & vice-versa

6 6.3 Average Speed

64-68 6.4 Relative Speed

6.5 Trains 6.6 Boats & Streams 6.7 Circular Motion

Ratio Proportion Variation & Partnerships

7.1 Simple Ratio & Compound Ratio

7 7.2 Conversion from Simple Ratio to Compound ratio

69-72 7.3 Ranking of Ratios

7.4 Proportions

7.5 Types of Proportions 7.6 Partnerships

Averages & Mixtures

8.1 Averages

8 8.2 Averages of Numbers in Arithmetic Progression

73-76 8.3 Deviation Method

8.4 Weighted Averages 8.5 Alligation



8.6 Mixtures

Permutation & Combination

9.1 Permutations

9.2 Arrangement of N things in N ways 9.3 Positive Conditions

9 9.4 Negative Conditions

77-79 9.5 Combined Conditions

9.6 Conditions collision 9.7 Circular Permutation 9.8 Combinations 9.9 Pigeonhole Principle

Probability

10.1 Probability

10.2 Problems on coins 10 10.3 Problems on dices 80-85

10.4 Problems on cards 10.5 Mutual Exclusion 10.6 Probability based on Permutation/Combination



Blood Relation

Independent Questions: -

Here the relationship between few people is given through a statement.

Now by drawing a tree diagram from the given statements we can define the relations between the

corresponding people.

Paragraph based Questions: -

Sometimes many statements are given in the form of a caselets which is then followed by a set of four

or five questions.

Solving the questions based on paragraph also include drawing tree diagram.

Symbolic relations based questions: -

Here certain symbols are used to describe different relations and then a statement is given relating

people using these symbols. Interpreting these symbols, we have to find the relation between the

people.

Frequently required relations on which questions are generally asked are given below:

Relation Gender Definition

By Ancestors

Father M Whom one is born to. Also called a parent.

Mother F Whom one is born to. Also called a parent.

Grand Father M Father of one‘s parent.

Grand Mother F Mother of one‘s parent.

Brother M Son of one‘s parents. Also called a sibling.

Sister F Daughter of one‘s parents. Also called a sibling.

Uncle (Paternal/Maternal) M Brother of one‘s parent. OR Husband of one‘s aunt.

Aunt (Paternal/Maternal) F Sister of one‘s parent. OR Wife of one‘s uncle.

Cousin M or F Child of one‘s uncle or aunt.

Nephew M Son of one‘s sibling.

Niece F Daughter of one‘s sibling.

Son M One‘s child.

Daughter F One‘s child.

By Marriage

Husband M Who one marries. Also called a spouse.

Wife F Who one marries. Also called a spouse.

Father–in–law M Father of one‘s spouse.

Mother–in–law F Mother of one‘s spouse.

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Brother–in–law M Brother of one‘s spouse. OR Husband of one‘s sister.

Sister–in–law F Sister of one‘s spouse. OR Wife of one‘s brother.

Son–in–law M Husband of one‘s daughter.

Daughter–in–law F Wife of one‘s son.

How to draw the tree diagram from given statements: - Following is the simplified procedure for drawing

and reading a family tree:

Choose convention for the genders. e.g. Circles for M and Squares for F.

To begin the tree, mark ―your‖ position or the position of the person for which maximum

information is given.

Mark all the other relations with respect to your position with proper conventions and

hierarchy.

All the relations who are at the immediate higher level than you are; are parents,

father/mother–in–law or uncles/aunts.

All the relations at the same level as you are; are either brothers/sisters, brothers/sisters–in–

law or cousins.

All the relations at the immediate lower level than you are; are sons/daughters,

sons/daughters–in–law, nephews/niece.

Mark Husband Wife relation by

Mark Siblings relation as

Mark Son, daughter relation as

Mark cousins as

For eg: A is husband of B, B is mother of C, C is sister of D and D is male cousin of E.

This will be represented as—

A B

C D E

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Questions

A is the sister of B, C is the father of B, D is the wife of C and E is the father of D. How is E related

to B?

1. Uncle 2. Grandmother 3. Father 4. Grandfather

Pradip goes to a party hosted by his brother Rahul who has a daughter Barkha. Barkha is dancing with

her brother Chandu. How is Anil related to Chandu?

1. Uncle 2. Nephew 3.Father 4.Cousin

A said to B, "Your only brother‘s son is my wife‘s brother". How is B related to wife of A?

1. Sister 2. Aunt 3. Mother 4. Daughter

A girl goes to watch a movie and sees a man sitting to her left. She found that the man was her relative.

The man is the husband of the sister of her mother. How is the man related to the girl?

1. Uncle 2.Nephew 3.Brother 4.Father

X and Y are brothers. P and Q are sisters. X‘s son is Q‘s brother. How is Y related to P?

1. Father 2.Brother 3.Grandfather 4.Uncle

My father‘s only brother‘s son‘s wife‘s brother-in-law is related to him as

1. Son 2.Uncle 3.Nephew 4.Grandfather

Pointing to a photograph a lady tells Manav, "I am the only daughter of this lady and her son is

your maternal uncle". How is the speaker related to Manav‘s father?

1. Cousin 2.Wife 3.Aunt 4.Daughter–in–law

Pointing to a woman in a photograph Ranbir said, ―She is the daughter of my grandfather‘s only son.‖

How is Ranbir related to that woman? 1. Uncle 2.Grandfather 3.Father 4.Sibling

Directions for Question 9-10: -

A, B, C, D, E and F belong to a family that has two married couples.

No one from the third generation is married.

C is F‘s mother–in–law.

D, E and B are A‘s teenaged elder sister, father and grand father respectively.

Which of the following is true?

1. A is C‘s wife 2.C is B‘s husband 3.D is E‘s daughter 4.D is E‘s son

10. Who is C‘s husband?

1. A 2.B 3.C 4.E

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Directions for Questions 11-15: -

L went to Nagpur to meet his brother M. M stays with his father N and Mother E. M‘s grandfather, F

also stays with him. M has two children X and Y. X‘s husband is U. Y is married to V, who is a

wrestler. C‘s son W welcomes L on his visit.

11. How is W related to X?

1. Niece 2. Nephew 3. Cousin 4. Son

12. How is E related to Y?

1. Mother 2. Grandmother 3. Aunt 4. None of these

13. How is M related to U?

1. Mother-in-law 2. Mother 3. Father-in-law 4. None of these

14. How is Y related to N?

1. Grandson 2. Granddaughter 3. Daughter 4. None of these

15. How is L related to F?

1. Grandson 2. Granddaughter 3. Daughter 4. None of these

Directions for Questions 16-20:

Six members of a family P, Q, R, S, T and U are Psychiatrist, Bank Officer, Advocate, Businessman,

Doctor and Consultant, in random order. The Doctor is the grandfather of U and he is a Psychiatrist.

The Bank Officer S is married to P. The Businessman R is married to the Advocate. Q is the mother of

U and T. There are two married couples in the family.

16. The profession of T is

1. Doctor 2.Bank Officer 3.Consultant 4.Psychiatrist

17. How many male members are there in the family?

1. Two 2.Three 3.Four 4.Cannot be determined

18. How is P related to T?

1. Grandfather 2. Grandmother 3.Father 4.Wife

19. By profession, P is

1. Advocate 2. Bank Officer 3.Consultant 4.None of these

20. Who are the two couples in the family?

1. SP & QR 2.PQ & RS 3.PT & TS 4.PR & QS

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Directions for Questions 21-24: - Read the following information and answer the questions that follow:

A*B means A and B are of the same age.

A–B means B is younger than A.

A+B means A is younger than B.

21. S*M–R is same as

1. R is the youngest. 2.R is the oldest. 3.M is younger than R. 4.None of these

22. X+Y+Z is same as

1. Y–X–Z 2.Z–Y–X 3.Z–X–Y 4.None of these

For an expression Amar–Akbar–Anthony, which of the following cannot be correct under any

circumstances?

1. Anthony is the father of Amar. 2. Anthony is the younger brother of Amar.

3. Amar is the father of both Akbar and Anthony. 4. None of these.

24. D–S*H is opposite to

1. H+S+D 2. H–S+D 3. S*H+D

1. 1 only 2.1 and 2 only 3.2 and 3 only4.None of these

Directions for Questions 25-30: - Use the relationships defined below to solve questions that follow.

A x B means A is the father of B. A - B means A is the mother of B. A B means A is the son of B. A= B means A is the daughter of B. A + B means A is the brother of B. A * B means A is the sister of B.

25. Which of the following means P is a sister of Q?

1. P + R - Q 2. Q – R * P 3. P Q + R 4. Q + P = R

26. Which of the following means R is a father of two children?

1. R * Q * P 2. R x P * Q 3. R * Q – P 4. R + P Q

27. Which of the following means P and Q are sisters? 1. Q * R – P 2. R – P * Q 3. Q = R – P 4. P * Q = R

28. Which of the following means P is a grandmother of R?

1. R + P Q 2. R * P – Q 3. Q – R = P 4. P – Q – R

29. Which of the following means Q is a paternal uncle of R?

1. Q + P x R 2. Q * P x R 3. Q P x R 4. R P * Q

30. Which of the following means R is a brother of P?

1. Q R – P 2. R Q - P 3. Q = P – R 4. P Q = R

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Directions

In this chapter we will be studying the concepts which involve a series of movements in specified directions and

of specified distances. Here the questions that are asked generally fall in the following two categories.

Type I- To find distances:-

The net distance travelled between the starting and ending points is asked. The ideal way of solving

such questions is to draw a diagram as you go on reading information about the problem and utilize

your knowledge to solve the question.

Most of the time, such questions will require the use of Pythagoras Theorem (Hypotenuse

2 = Base

2 +

Height2). Hence, the key is to know as many Pythagorean Triplets as possible for quickest solution

of the problem. Type II- To find directions:-

These questions have an individual moving about in a given direction and then turning in a specified

direction for one time or more. Finally the question asks us to find the direction in which the person is

moving or standing with respect to the original direction.

Type III- To find distances & directions both: -

There may be a few questions which may ask both the directions and the distances. It‘s just the combination of both the above types in the same question.

Fig. of Directions: -

The fig. given below shows the 4 main and 4 sub-directions which are North, East, West & South and

North-East, South-East, North-West & South-West.

To remember the diagram easily, observe the diagram carefully and you will come to know that it

makes NEWS in zigzag form.

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Questions

Jatin travels a distance of 3m north, then travels 3m west, then turns left and travels 12m and finally turning left travels 15m. What is the approximate distance of the place he reached from his original

place? 1.15m 2.21m 3.20m 4.35m

Sonal starts from her house, travels 5 km to the west, then travels 7 km to the right and then travels 4 km to the left after which she travels 2 km south and finally travels 3 km west. How far has she

travelled from his house? 1.14 km 2.13 km 3.10 km 4.15 km

Sameer travels 5 km towards the west and then travels 18 km towards the left; he then travels 7 km to

the right and then travels 6 km towards the left and finally travels 2 km towards the east. How far is he from the starting point in vertical direction?

1.7 km 2.21 km 3.15 km 4.26 km

Sahil travels 12 km in the south and then travels 5 km to the right and then travel 15 km towards the right and finally travels 5 km towards the east .How far is he from the starting place?

1.28 km 2.11 km 3.3 km 4.5 km

Gopi starts from his house and travels 10 km towards south and then turning right he travels 4 km. He

then turns left and travels 7 km, again travels 7 km left and finally travels 17 km to the left. How is he from his original place?

1.5 km 2.6 km 3.7 km 4.3 km

Aditya travels 6 km west, then 10 km south, then travels 3 km towards east, and then 10 km north and

finally goes 5 km west. How far is he from the starting place? 1.9 km 2.7 km 3.8 km 4.10 km

Varsha walks 10 meters straight and 10 meters towards her right. After that she walks 5, 15 and 15

meters respectively, every time turning to her left. How far is she from the starting point? 1. 5m 2.10m 3.15m 4.20m

Shalini travelled a distance of 100 m in a straight line. She turned right and walked 60 m, then again turned right and walked 80 m. Finally, she turned right and walked 60 m. How far is she from the

starting point? 1.20 m 2.30 m 3.10 m 4.40 m

I am facing North. I turn left and walk 20 m. Then I turn left again and walk 10 m. Then I turn right

and walk 10 m and then turning left walk 20 m. Then I turn left again and walk 60 m. In which

direction I am from the starting point? 1. East 2.North–West 3.South–East 4.West

Ritika walks 10 km from to south and turns left and walks 5 km, and then she turns left and walks 8

km. In which direction is she now with respect to the starting point? 1. East 2.South-East 3.North 4.North-East

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Directions for questions (11-14): -

If you start running from a point towards north and after covering 4 km you turn to your left and run 5

km, and then again turn to your left and run 5 km and then turn to left again and run another 6 km and

before finishing you take another left and run 1 km then answer the following questions.

11. How many km are you from the place you started?

1. 1 2.3 3.5 4.None of these

12. In which direction will you be running while finishing? 1. East 2.West 3.North 4.South

13. After taking the second turn, in which direction will you be running? 1. East 2.West 3.North 4.South

14. In which direction you have to move if you want to go to starting point again? 1. East 2.West 3.North 4.South

15. Rishi travels 10 km towards south. He then turns left and travels 2 km and then turns right and travels 4

km and finally travels 2 km towards the east. What is his position with reference to the starting point?

1.4 km E, 14 km S 2.14 km S, 4 km E 3.18 km S, 14 km E 4.18 km S, 8 km E

A person travels 4 km towards the east and then travels 3 km towards the left. How far and in what direction is he from the original point? 1. 7 km North-East 2.5 km North-East 3.7 km South-West 4.5 km South-West

Deepika travels 6 km towards east, then 5 km towards north, and finally travels 6 km towards east.

How far is he from his original place and in what direction? 1.13 km N-E 2.8 km N-W 3.11 km W 4.17 km W

Salman travels 6 km towards east, and then 9 km towards south, then travels 1 km towards left and then

9 km towards north, and finally travels 11 km towards west and reaches Katrina‘s house. How far is he from his original place and in what direction?

1.4 km W 2.17 km E 3.3 km W 4.16 km E

19. If you start from your house and go 15 km north, then travel 4 km to left, and then 5 km towards the left, then again travels 10 km towards the left, and then 18 km towards the right. How far are you from your house and in what direction?

1.19 km, S-E 2.10 km, S-E 3.19 km, N-W 4.10 km, N-W

20. Priyanka starts from her house and walks 30 km south, then travels 8 km to the right and then 10 km towards the right, then again travels 20 km towards the right and then 36 km towards the left. How far is she from her house and in what direction?

1.20 km, N-E 2.20 km, N 3.20 km, E 4.20 km, S-E

21. A wall clock shows 8.30. If the minute hand points towards east, in what direction will the hour hand point? 1. South-West 2.South-East 3.West 4.North-West

22. If South-East becomes North, North-East becomes West, and so on, what will South become? 1. South-West 2.South-East 3.North-East 4.North-West

23. A is 40 m South–West of B. C is 40 m South–East of B. C is in which direction of A? 1. East 2. West 3.North–East 4.South

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Coding-Decoding

Useful Table for coding-decoding: -

The table given below is very much helpful for questions of coding-decoding & Alphabetic Series.

1 2 3 4 5 6 7 8 9 10 11 12 13

A B C D E F G H I J K L M

Z Y X W V U T S R Q P O N

26 25 24 23 22 21 20 19 18 17 16 15 14

Coding for shifting Letters: -

In this type of coding we obtain the code for particular letter by shifting it backward or forward.

Shifting may have any logic it may be either backward or forward or may be combination of both.

For E.g. If DAD is coded as EBE then find the code for TIGER.

Now we can clearly observe that the coding is done by shifting the letter in forward direction by 1 &

hence TIGER=UJHFS

Coding with Mathematical operators: -

In this type of coding mathematical operations like addition, subtraction, multiplication or division are

performed on position of letters to give a code

For e.g. if CAT is coded as 24 then find the code for FAR.

Now observe that coding is done by adding the corresponding positions of C=3, A=1 & T=20 i.e.

3+1+20=24 similarly we can say that FAR= F (6) + A (1) + R (18) = 6+1+18=25.

Coding with Opposite Letters: -

In this type of coding letters are coded by their opposite letters in above given table Like A=Z, B=Y

and so on.

For E.g. If code for MOUSE=‖NLFHV‖ then find the code ROSE

Now we can clearly observe code for MOUSE is obtained by taking the opposite letters in the above

table i.e. NLFHV similarly we can take R=I, O=L, S=H & E=V and hence code for ROSE=‖ILHV‖.

Coding with shuffling letters: -

In this type of coding the letters in the given word are shuffled and code is formed.

For e.g. if MOTHER is coded as MROETH then find the code for FATHER

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Now we can observe the coding is done by shuffling the letters of MOTHER in such a way that First

and Last are taken together similarly second-second last & so on, hence code for FATHER=FRAETH.

Coding with random Letters: -

In this type of coding you will see the particular letter is coded as any other random letter

For E.g. Code for BLADE=‖SPTFA‖ then find the code for BAD

Now we can clearly see B=S, L=P, A=T, D=F & E=A and hence BAD=STF

Coding with random Numbers: -

In this type of coding we have some random numeric code assigned to particular letter of word from

which we have find the code for another given word.

For e.g. TRAIN=1235 then find the code for TAN, we can clearly say it will be equal to 135.

Coding with Corresponding words: -

In this type of coding a particular word is used for another word.

For e.g. if ‗I am great‘ is coded as ‗tir spa pul‘ & ‗I ate apple‘ is coded as ‗spa wen tek‘ then find the

code for I?

Now we can clearly see that the common word in coded language is spa & hence we can say that code

for I=spa

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Questions Directions for questions 1-4: -

In a certain language if the word CHAIR is coded as RIAHC, then how will you code the following words?

TABLE

(1) ELTAB (2) ELABT (3) ELBAT (4) None of these

STOOL

(1) LOOTS (2) LOOST (3) LOSOT (4) None of these

BENCH (1) HCBEN (2) HCNEB (3) HCENB (4) None of these

DESK

(1) KESD (2) KSDE (3) KEDS (4) None of these

Directions for questions 5-8: -

In a certain language if the word CLASSIC is coded as DMBTTJD, then how will you code the following words?

FUTURE (1) GVUVSF (2) GVVUSF (3) GVUVTF (4) GUVUSF

RETRO

(1) SFUSP (2) SUFSP (3) SFUSF (4) SFSFU

GROUP (1) HSPQV (2) HSPVQ (3) HSQVP (4) HSTVQ

COLD

(1) EDPM (2) DEPM (3) DPEM (4) DPME


In a certain code language, EXAMINATIONS is coded as 123456375869. Find the appropriate codes for the following words.

NOMINATE (1) 68546371 (2) 68456371 (3) 86456371 (4) 68456351

10. TIME (1) 7451 (2) 7641 (3) 7541 (4) 7341

11. MATS (1) 4369 (2) 4378 (3) 4359 (4) 4379

12. STAMINA (1) 9735563 (2) 9726543 (3) 9745463 (4) 9734563


If PEON is coded as ODNM, then find out the codes of the words in the following

13. MOTEL

(1) LNSKD (2) LNDSK (3) GNSBK (4) LNSDK

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14. SPOUSE (1) RONDRD (2) RONTRD (3) RONTRR (4) RONDRT

15. PRIVATE (1) OQUHZSD (2) OQHUYSD (3) OQHUZSD (4) OQHUASD

16. GENERAL (1) FDNDQZK (2) FDNDPZK (3) FDNDRZK (4) FDNDQAK

17. If DAD=9 & COW=41 then TIGER=_______? (1) 62 (2) 69 (3) 59 (4) 52

18. If ADARSH = 45, STOOL = 76, then COLLEGE = _____? (1) 62 (2) 69 (3) 59 (4) 52

19. In a certain code language GOD = 29, and ANGEL = 44, then SHAITAN = _____? (1) 79 (2) 63 (3) 50 (4) 56

20. If COW=51 & GOD=36 Find the code for DAD? (1) 9 (2) 12 (3) 14 (4) None of these

Directions for questions 21 to 30: -

Each letter of the alphabet series is coded as follows: A Z, B Y, Z A. For decoding a reverse process is

followed i.e. Z A, Y B, A Z. Based on this answer the following.

21. Which word is the code as ―RMGVIMVH‖?

(1) INTERNET (2) INTRANET (3) INTENDED (4) INTERNES

22. Which word is code as ―IVZK‖? (1) REAP (2) ROLE (3) REEL (4) REEM

23. What is the code word for ―LAPTOP‖? (1) OZKGLK (2) OZKLHK (3) OZKGIK (4) OZLGIK

24. What is the code word for ―ISRO‖? (1) RHIJ (2) RSIL (3) RHIL (4) RVIL

25. Which word is code as ―KRIEZGV‖? (1) PREVENT (2) PRETEND (3) PRESENT (4) PRIVATE

26. What is the code word for ―MONITOR‖? (1) NLMRGIK (2) NLMRLGK (3) NLMRGLI (4) NLMKGKI

27. What is the code word for ―MANAGEMENT‖? (1) NZMZTUMUNG (2) NZMZTVNVMG (3) NZMZSVMMG (4) MZMZTVMVMG

28. What is the code word for ―FLOPPY‖? (1) UOLKKB (2) UOMKKB (3) UOLKKR (4) UOLRKB

29. What is the code word for ―COMPUTE‖? (1) XLNGFGV (2) XLNKFGV (3) XLNKKVI (4) XLMKFGV

30. Which word is the code as ―RNNVIHV‖? (1) IMMERSE (2) IMPOUND (3) IMMENSE (4) IMPULSE

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If Fruits are sweet is coded as 547; Lets have Fruits is coded as 325; Fruits have Vitamins is coded

as 526, then Vitamin =? (1) 4 (2) 5 (3) 6 (4) 3

If Paper is tough is coded as 138; Solve the paper is coded as 521; Tough paper tests is coded as

816, then Tests =? (1) 8 (2) 6 (3) 7 (4) 5

33. In a certain code YELLOW is coded as 956612, then LOWLY is coded as (1) 62196 (2) 61269 (3) 92196 (4) 91296

34. If TELEPHONE is coded TEENLOEHP, then the code for TELECOM will be? (1) TMELOEC (2) TMEOLCE (3) TMELOCE (4) TMEOLEC

35. If RAHUL is coded as AURHL then find the code for GIRISH? (1) GRSIIH (2) IIHGRS (3) IIGRSH (4) IGIRHS

36. In a certain code language, ‗dom pul ta‘ means ‗bring hot food‘, ‗pul tir sop‘ means ‗food is good‘ and `tak da sop‘ means ‗good bright boy‘. Which of the following does mean ‗is‘ in that language? (1) dom (2) pul (3) to (4) tir (5) Cannot be determined

In a certain code language, ‗XZM‘ means ‗He is bright.‘, ‗TCZO‘ means ‗Every lawn is green.‘ and ‗OQCN‘ means ‗Every wall was green‘. Which of the following means ‗Every lawn is bright‘ in that language?

(1) ZTOM (2) CXZT (3) XOTZ (4) CZOT (5) Cannot be determined

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Alphabetic Series

Letter Series: -

In this type of problems some alphabets are given in series which follows a particular sequence and we

have to find which alphabet can be a part of this series.

For Find the answer for E.g. A,C,E,G,_ , now we can see very clearly that these are all odd numbered alphabets i.e. 1,3,5,7 so the next would be alphabet 9 i.e. I

Odd Man Out: -

In these type of questions 4-5 alphabets or 4-5 words will be given to us out of which all but one follows a particular pattern or satisfy a particular condition and we have to find out the one which does not follow that pattern or does not satisfy the condition.

For e.g. Find the odd man out amongst A, Z, E, O & U. Now in these given alphabets all are vowels

except Z and hence Z is the answer.

Pattern Series: -

In these type of questions a particular pattern is given whose alphabets are missing in series and we

have to first identify the pattern and then the missing alphabet‘s

For e.g. find the missing alphabets in ―a_cd_b_dab_d‖ now in these series the pattern is ―abcd‖ is recurring and hence the answer is ―bacc‖.

Letter Analogy: -

ere the questions are similar to number analogy and are based on the relationship exhibited by the two groups of letters on each side of the sign :: . Generally, three pairs of letters are given followed by a question mark or a blank space. The student has to identify the relation and find the fourth group of letters that will replace the question mark or the blank.

Page | 14



Questions

DIRECTIONS for questions 1 to 10: - Find the next term of the following series.

B, D, G, I, L, N, ? (1) O (2) Q (3) S (4) U

X, U, S, P, N, K, I, ?

(1) J (2) K (3) M (4) F

A, C, E, G, I, ? (1) H (2) J (3) K (4) L

D, I, L, Q, T, Y, B, G, ?

(1) H (2) I (3) O (4) J

Y, W, U, S, Q, ?

(1) P (2) O (3) M (4) B

D, F, I, M, R, ? (1) S (2) U (3) T (4) X

LXF, MTJ, NPN, OLR, ?

(1) PHV (2) PPV (3) PIU (4) PJW

ABY, CDW, EFU, GHS, ____

(1) IJK (2) IJQ (3) IKP (4) IJR

AIU, CKW, ____, GOA

(1) ENY (2) EKY (3) EMY (4) EGS

10. TGS, RIQ, _____, NMM (1) KOP (2) OPK (3) POK (4) PKO

DIRECTIONS for 11-17: -

Find the odd man out amongst the following

11. (1) GJL (2) MPS (3) SVX (4) LOQ

12. (1) GIK (2) LNP (3) YAC (4) SUV

13. (1) SUTR (2) TVXZ (3) UWYA (4) WYAC

14. (1) TREAT (2) TEARS (3) THINK (4) TRAIT

15. (1) I (2) L (3) D (4) Y

16. (1) AZ (2) GS (3) JQ (4) DW

17. (1) IO (2) EO (3) OU (4) AE

DIRECTIONS for 18-20: -

Understand the pattern and find the missing letters.

18. ab_d_bc_a_c_ab_d (1) cadbdc (2) cabbcd (3) abbcdd (4) caddbc

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19. a_b_cc_ _dd_eeee (1) abcdd (2) bcddd (3) bcdde (4) bcdee

20. abca_bcaab_ca_bbc_ (1) ccaa (2) bbaa (3) abac (4) abba

Directions for 21-23: -

Find the second pair after determining the relation between the first pair in the given questions.

21. AEH : ZVS : : DGL:____

(1) WHO (2) VPN (3) WTO (4) VPT

22. LN : OR : : JL :____ (1) OM (2) MP (3) OP (4) PM

23. CGH : FKM : : JLN:____ (1) NTS (2) MPS (3) MQT (4) NRS

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Number Series

Gradually Increasing/Decreasing Series: -

In this type of series you will find the numbers are increasing gradually e.g. 2, 3, 5, 8, 12, 17…… in

this particular series we can see that numbers are not increasing drastically but they are increasing gradually.

If you find this type of series in the question paper you can think that the logic can be addition or

subtraction.

As you can see in the example given above numbers are increasing by 1, 2, 3……….

Drastically Increasing/ Decreasing Series: -

In this type of series you will find the numbers are increasing drastically e.g. 1, 2, 6, 24, 120…… in

this particular series we can see that numbers are increasing drastically.

If you find this type of series in the question paper you can think that the logic can be multiplication or division.

As you can see in the example given above numbers are multiplied by 1, 2, 3……….

Alphanumerical Series: -

In this type of series alphabets and numbers are taken together to form a particular series for e.g. if we this series A2, B4, C6, D8, E10………. Now in this type of series we can see that the numbers are increasing by 2 & letters are increasing by one.

These series are relatively simple because complex logic is generally avoided in these types of series.

Alternating Series: -

Alternating series is combination of two or more series.

The two series which are combined will be simple series but combination of two series will make the series look strange.

For e.g. 1, 2, 2, 4, 3, 6, 4, 8……….. now in this series if we observe carefully we will be able to notice

that it is combination of two different series i.e. 1, 2, 3, 4…… & 2, 4, 6, 8……..

Number Analogy: -

Analogy basically means similar items. Here questions contain a pair of numbers that are related in some way. They are followed by a third number. Analyzing the logic, the student is expected to find the fourth number that is related to the third number in the same way as the first two numbers.

Generally, the numbers in a given pair are related by the following logic:

One number is a multiple or factor of the other.

One number is the square or square root of the other.

One number is the cube or cube root of the other.

One number is obtained by adding or subtracting the digits of the other.

The numbers are primes, consecutive, even or odd numbers.

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Methodology for tackling the number series questions:

First observe the difference between the two successive terms. If the difference is fixed (constant), then

it is a fixed difference series.

If the difference is changing by a fixed number, then it is an increasing or a decreasing series with a

constant difference.

If the difference is increasing or decreasing very rapidly, then probably it is a multiplication or division

series.

If the difference increases and decreases alternately, then it‘s a combination of two or more series.

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Questions

2, 7, 14, _, 34, 47 (1) 29 (2) 27 (3) 31 (4) 23

2. 6, 9, 13, 18, _,31, 39 (1) 22 (2) 23 (3) 24 (4) 25

3. 15, 35, 63, 99, _ (1)141 (2) 147 (3) 143 (4) 145

4. 5, 9, 16, 29, 54, 103, _ (1)102 (2) 94 (3) 103 (4) 200

5. 2, 12, 30, 56, 90,_ (1)121 (2) 132 (3) 144 (4) 126

6. 22, 24, 28, 36, 52, _ (1)74 (2) 94 (3) 84 (4) 104

7. 7, 24, 75, 228, _ (1)748 (2) 687 (3) 684 (4) None of these

8. 10, 21, 34, 49, 516, 625, _

(1) 936 (2) 736 (3) 749 (4) 763

9. 3, 12, 4, 5, 30, 6, 7, _, 8, 9, 90, 10 (1)55 (2) 56 (3) 57 (4) 46

10. 2, 3, 5, 6, 7, 13, 8, 9, ___ (1)17 (2) 19 (3) 21 (4) 23

11. 17, 19, 14, 16, _13, 8 (1)12 (2) 11 (3) 14 (4) 15

12. 9, 6, 16, 10, 30, 18,_, 34 (1)36 (2) 60 (3) 58 (4) 60

13. 1, 3, 2, 4, 6, 7, 15, 12, 33, 19, 56, 28 … (1) 4 (2) 15 (3) 33 (4) 56

14. 8, 9, 8, 7, 10, 9, 6, 11, 10, _____, 12 (1)5 (2) 7 (3) 8 (4) 11

15. 2, 5, 15, 60, 280, _

(1) 1735 (2) 1235 (3) 1275 (4) 1375

16. A3, D4, G5, J6, _ (1) N7 (2) N8 (3) M8 (4) M7

17. AB5, EF8, IJ11, MN14, _ (1) OP17 (2) LN17 (3) PQ17 (4) QR17

18. IV6, V7, VI8, VII9, VIII10, _ (1)IX11 (2) X11 (3) IX9 (4) X10

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Directions for 19-25: - Select the related number from the given options.

19. 343 : 512 :: 1000 : _

(1)1331 (2) 1210 (3) 1321 (4) 1421

20. 36 : 18 :: 72 : _ (1)24 (2) 54 (3) 134 (4)164

21. 28 : 21 :: 40 : _ (1)30 (2) 25 (3) 32 (4) 27

22. 124 : 8 :: 321 : _ (1)6 (2) 5 (3) 4 (4) 7

23. 123 : 6 :: 345 : _ (1)8 (2) 10 (3) 320 (4) 12

24. 123 : 14 :: 241 :_ (1)17 (2) 21 (3) 24 (4) 19

25. 225 : 196 :: 961 : _ (1)625 (2) 900 (3) 361 (4) 128

Directions for 26-30: - Find the odd man among the following.

26. (1)24 (2) 21 (3) 19 (4) 6

27. (1)8 (2) 27 (3) 9 (4) 1

28. (1)8 (2) 2 (3) 5 (4) 7

29. (1)81 (2) 25 (3) 75 (4) 90

30. (1)125 (2) 75 (3) 175 (4) 140

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Set theory & Venn Diagrams

Introduction to set theory: -

Set: A set is a ―well defined‖ collection of objects. Here the term ―well defined‖ is important. For a ―well defined‖ set, one is able to tell clearly whether a random element ―x‖ is a member of the set or not. e.g. Set of all the vowels is a ―well defined‖ set because one can easily tell whether ‗b‘, ‗e‘, ‗r‘, ‗1‘, ‗0‘ etc. are a member of the set or not. Set of seven numbers is not ―well defined‖ since we don‘t know which seven numbers are we talking about. Sets are represented in two forms:

Roster/Tabular form: All the elements of the set are listed inside curly

brackets. e.g. A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

Set Builder/Rule form: Here we define the set by writing the properties which are shared by all or some of the elements of the set

e.g. A = {x| x is a prime number less than 30}

Venn Diagrams: Sets can also be represented using geometrical figures like circles,

rectangles, triangles etc.

e.g. Universal Set

A 2, 3, 5, 7,

11, 13, 17,

19, 23, 29 Venn diagrams are the most useful tool for solving questions based upon set theory. Interaction between two sets: Any two sets A and B can any one of the following interaction between them based on the conditions given: Both the sets are some distance apart. There is no element common between them.

A B

Both the sets intersect each other. There is at least one element which is common to them. A

B

The intersection is the region of common elements. One set is contained inside the other. All the elements of one set are common to the other one.

A B

B A

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Questions Directions for questions 1-4: -

In a class, 42 of students like cricket, 5 of students like cricket and football and 10 like none. If 96 students like only football

What is the strength of the class?

(1) 100 (2) 150 (3) 200 (4) None of these

How many like at least one game? (1) 170 (2) 10 (3) 20 (4) 180

How many students like exactly one of the two games?

(1) 170 (2) 10 (3) 20 (4) 180

How many students like neither cricket nor football?

(1) 5 (2) 20 (3) 10 (4) 180


Of the members of a school sports team 21 are on the basketball team, 26 on the hockey team and 79 on the football team. 14 play hockey and basketball, 15 play hockey and football and 12 play football and basketball, 8 are on all the three teams.

How many members are there in altogether?

(1)47 (2)43 (3) 93 (4) None of these

How many plays only basketball?

(1)3 (2)9 (3) 17 (4) 21

How many plays exactly two games?

(1)17 (2)25 (3) 38 (4) 63

How many plays exactly one game?

(1)27 (2)35 (3) 68 (4) 60


The findings of a survey for three magazines A, B and C are as follows: 50% people read magazine A, 35% people read magazine B and 36% people read magazine C, 10% people magazines A and B, 8% people read magazines B and C and 3% people read all the three magazines. Every person in the survey

reads at least one of the three magazines.

Find the percentage of people who read magazines A and C. (1)3 (2) 6 (3) 8 (4) 10

10. Find the percentage of people who read only magazine A. (1)37 (2) 35 (3) 47 (4) 50

11. Find the percentage of people who read at least two magazines. (1)15 (2) 18 (3) 20 (4) None of these

12. Find the percentage of people who read only one magazine. (1)75 (2) 82 (3) 57 (4) 85

13. Find the percentage of people who read only two magazines. (1)15 (2) 18 (3) 16 (4) None of these

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14. A company manufactures boxes, 60% boxes are red in color and rests are blue in color. 40% of the

boxes have length 3cm while rest have 5cm length, if 20% of the boxes are red & length 3cm then what % of total boxes are blue & have length 5cm.

(1)15 (2) 18 (3) 16 (4) None of these

Of 30 mice, 10 are white in color, 21 have tail, and 5 are not white in color and do not have tail. How

many of the mice are white & have tail (1)15 (2) 5 (3) 6 (4) None of these


Each of these questions below contains three groups of things. You are to choose from the following four numbered diagrams, the diagram that best depicts the correct relationship among the three groups of things in each question.

1) 2) 3) 4)

Alphabet, Vowels, Numbers

Natural Numbers, Prime Numbers, Composite Numbers

Tennis Fans, Cricket Players, Students

Table, Chair, Furniture

Mumbai, India, USA

Vegetables, Tomatoes, TV

Tiger, Elephant, Animal

Male, Female, Human

Rational numbers, Real numbers, Imaginary numbers

Egg, Veg food, Non-veg food

Directions for 26-31: - In the following figure the triangle represents team leaders, the circle represents managers and the rectangle represents BE (IT). Study the figure carefully and answer the questions which follow.

26. Which numbered space represents team leaders who are managers and BE (IT) also?

(1)2 (2) 3 (3) 4 (4) 5

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27. Which numbered space represents BE (IT) who are managers but not team leaders?

(1)6 (2)7 (3) 8 (4) 4

28. Which numbered space represents BE (IT) who are neither managers nor team leaders? (1)1 (2)2 (3) 3 (4) 4

29. Which numbered space represents team leaders who are neither managers nor BE (IT)? (1)2 (2) 4 (3) 3 (4) 5

30. Which numbered spaces represent managers who are neither BE (IT) nor team leaders? (1)1, 2 (2) 3, 4 (3) 6, 7 (4) 7, 8

31. Which numbered space represents team leaders who are managers but not BE (IT)? (1)2 (2) 3 (3) 4 (4) 5

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Syllogisms

A deductive argument is one in which the conclusion follows with logical necessity from the premises. If the premises are true and the inference valid, then it is logically impossible that the conclusion be false.

A categorical syllogism is a deductive argument with two categorical premises and a categorical

conclusion. For eg.

All soldiers are patriots --- Premise 1 No traitors are patriots --- Premise 2 Hence, no traitors are soldiers ---Conclusion

The bold words are the terms in the syllogism. Notice that each of the two premises and the conclusion have two terms each, and the syllogism has exactly three terms—soldiers, patriots and traitors.

For diagramming a categorical proposition, we use shading or the mark ―A‖. The following convention is used.

If a circle or a part of a circle is shaded then the shaded area is empty. If a circle or a part of a circle has ―A‖ in it then that area is not empty. If a circle or a part of a circle is neither shaded nor has a cross in it then nothing can be said about that

area.

Standard Form of Syllogism

There are four standard forms of syllogism. They are diagrammed as follows:

All P are Q.

Here we shade that part of circle P which is not overlapping with the Q circle, signifying that this area is empty.

No P are Q.

Here we shade that part of circle P which is overlapping with the Q circle, signifying that this area is empty.

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Some P are Q.

Here we put an ―A‖ in the area of circle P overlapping with circle Q, signifying that this area is not empty.

Some P are not Q.

Here we put an ―A‖ in the area of circle P not overlapping with circle Q, signifying that this area is not empty.

Sometimes we also come across some non-standard statements. In such as case, we convert them into standard syllogisms using the following rules.

If any term is not prefixed by ―some‖ or ―all‖, then assume it is ―all‖ and proceed.

Statement like ―All chairs are not tables‖ are interpreted as ―No chair is a table‖

Statement like ―Not all chairs are tables‖ are interpreted as ―Some chairs are not tables‖

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Questions

Directions for questions 1-15: -In the following questions, two statements are followed by two conclusions. Mark your answer as

If only conclusion I follows.

If only conclusion II follows.

If both the conclusions follow.

If none of the conclusions follow.

1. Statement I: All fish are snakes.

II: No snakes are sparrows.

Conclusion I: No fish is a sparrow.

II: No sparrow is fish.

2. Statement I: Some black is pigeons.

II: All pigeons are yellow.

Conclusion I: No black is yellow.

II: No yellow is black.

3. Statement: I: Some cats are dogs.

II: No dogs are rats.

Conclusion I: Some cats are rats.

II: No cats are rats.

4. Statement I: Some comets are stars.

II: Some stars are planets.

Conclusion I: Some comets are planets.

II: Some planets are comets.

5. Statement I: No girls are intelligent.

II: Some intelligent are nice.

Conclusion I: No girls are nice.

II: Some girls are nice.

6. Statements I: All diamonds are stones.

II: No stone is glass.

Conclusions I: No diamond is glass.

II: No glass is a stone.

7. Statements I: All fish are hens.

II: All hens are boys.

Conclusions I: All fish are boys.

II: All hens are fish.

8. Statements I: All cards are notes.

II: No note is a page.

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Conclusions I: Some cards are pages.

Some pages are notes.

9. Statements I: All players are females.

No female is smart.

Conclusions I: No player is smart.

No male is in the team. 10 Statements I: Some cows are cars.

'X' is a cow.

Conclusions I: 'X' is not a cow.

Some cars are not cows. 11. Statements I: All fathers are sons.

All sons are grandfathers.

Conclusions I: All grand fathers are fathers.

All fathers are grandfathers. 12. Statements I: Some trains are trees.

No tree is a picture.

Conclusions I: Some trains are pictures.

No train is a picture. 13. Statements I: Some trays are fans.

All fans are bottles.

Conclusions I: No bottle is a tray.

Some trays are bottles. 14. Statements I: Some books are toys.

No toy is red.

Conclusions I: Some books are red.

Some books are not red. 15. Statements I: Some rivers are seas.

All seas are skies.

Conclusions I: All skies are seas.

Some rivers are skies.

Directions for questions 16-20: - In each of the following questions, read the two statements and the four conclusions. Choose the correct answer option. 16. Statement I: Some boats are cars.

No car is bike.

Conclusion I: No car is boat.

No boat is car.

Some cars are bikes.

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IV: Some boats are bikes.

a) Either III or IV b) Either II or III c) Either II or IV d) None follows

17. Statement I: Some books are biscuits.

II: All biscuits are pastries.

Conclusion I: All pastries are biscuits.

II: All books are pastries.

III: Some books are pastries.

IV: Some biscuits are not books.

a) I and II only b) None follows c) All follow d) III only

18. Statement I: All bushes are trees.

II: No tree is green.

Conclusion I: Bushes and trees are not green.

II: No bush is green.

III: No tree is a bush.

IV: Some bushes are not trees.

a) IV only b) III only c) I only d) I and II only

19. Statement I: All players have caps.

II: Players with caps rock.

Conclusion I: All rocking players have caps.

II: All players with caps are rocking players.

III: No player with a cap rocks.

IV: No rocking player has a cap.

a) I only b) III only c) I and II only d) None of these

20. Statement I: Some tomatoes are peas.

II: Some peas are beans.

Conclusion I: Some tomatoes are beans.

II: All beans are tomatoes.

III: Some beans are tomatoes.

IV: Some peas are tomatoes.

a) I only b) II only c) III only d) IV only

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Clocks & Calendars

Clocks: -

The face of a clock is a circle whose boundary is divided into 60 equal parts, called minute spaces.

Since the angle in a circle is 360o

, each minute space makes an angle of 60 at the center of the dial.

The face of the clock is divided into 12 equal parts called hour spaces. Each hour space has an angle

of 300 at the center of the dial. Thus, 5 minute spaces make 1 hour space.

The clock has two hands-the smaller one, called hour hand & the longer one called the minute hand.

Even though some clocks have a third hand called second hand, we will ignore it for our discussion purpose.

The minute hand completes one rotation or moves through an angle of 360o

in 60 minutes. Therefore,

the angular speed of the minute hand is 60 per minute.

The hour hand completes one rotation or moves through an angle of 360o

in 12 hours. Therefore, the

angular speed of the hour hand is 1/20 per minute.

Since both the hands move in the same direction their relative speed is 5.5

0 per minute.

The minute hand gains 55 minutes on the hour hand in one hour.

If both the hands start together from the same position, both hands will coincide after 65 minutes.

If the hands meet before 65 minutes then the clock gains time or it runs fast. If the hands meet after 65

minutes then the clock loses time or it runs slow.

Formula: θ = where θ is angle between hour hand and minute hand is minutes and

is hours.

ANGLE BETWEEN THE HOUR AND MINUTE HANDS OF A CLOCK AND THEIR

FREQUENCY

POSITION EXAMPLE EACH EVERY 12 EVERY 24

HOUR HOURS HOURS

Straight Line (Angle = 180o

) 6 o‘clock Once 11 Times 22 Times

Coinciding (Angle = 0o

) 12 o‘clock Once 11 Times 22 Times

Right Angle (Angle = 90o

) 3 o‘clock Twice 22 Times 44 Times

Calendars: -

Calendars involve the method of finding a particular day of the week on a particular given date. The process of finding the day lies in obtaining the number of odd days. The number of days in excess of the complete number of weeks in a given period are called odd days.

A year will be called leap year if it is divisible by 4. For example, 1944, 1964,1996 etc. For a century

year to be the leap year it must be divisible by 400. Thus years 400, 800, 1200, 1600, 2000 are leap years.

An ordinary year has 365 days. To get the odd days, we divide 365 by 7 to get the complete number of

weeks and the remainder will be the odd days. As 365 = (7x52)+ 1, ordinary year will have 1 odd day. Since a leap year has 366 days, hence a leap year has 2 odd days.

Page | 30



Odd days in a century:

100 years = 76 ordinary years + 24 leap years (Note that 100/4=25, but as 100th

year is not divisible by 400, we have only 24 leap years).

100 years = (76x1)+(24x2)= 76+48 = 124 =(7x17)+5. Hence, every 100 years will have 5 odd

days.

Similarly, in 200 years there will be 2x5=10=(7x1)+3=3 odd days. in 300 years there will be 3x5=15=(7x 2)+ 1=1 odd day. in 400 years there will be 4x5+1 (leap year) = 21 = 7x3=0 odd days. Thus, 800, 1200, 1600, 2000 years will leave 0 odd days.

In a nutshell-

Years Number of Odd Days

Ordinary 1

Leap 2

100 5

200 3

300 1

400 0

Example Number of Odd days

1999 1

1996 2

1700 5

1800 3

1900 1

2000 0

The day of the week is counted according to the number of odd days left.

Odd days left Day of the week

0 Sunday

1 Monday

2 Tuesday

3 Wednesday

4 Thursday

5 Friday

6 Saturday

The following data gives the months in which the same calendar can be used, i.e., the corresponding dates of the months fall on the same week day.

Leap Year January & July, February & August Non-Leap year January & October, February & March Leap or non-Leap March & November; April & July, September & December

Two non-leap years OR two-leap years will have the same calendar if the number of odd

days of the completed years are equal. For example, for ordinary years, the same calendar can be used for 1971, 1982, 1993 and 1999. For leap years, the same calendar can be used for the leap years 1972 and 2000.

The Last day of a century cannot be a Tuesday, a Thursday or a Saturday.

The First day of a century must be a Monday, a Tuesday, a Thursday or a Saturday.

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Questions What is the angle between the two hands of a clock shows 7.30 p.m?

(1) 150 (2) 30

0 (3) 45

0 (4) None of these

What is the angle between the two hands of a clock, when the time is 8.20 p.m?

(1) 1100 (2) 120

0 (3) 130

0 (4) 140

0

At 6.15 , the hour hand and the minute hand of a clock form an angle of

(1) 900 (2) 91.5

0 (3) 94.5

0 (4) 97.5

0

At what time between 9 O‘clock and 10 O‘clock are the hands of a clock in the opposite direction?

(1)9hrs. 21 8/11min (2)9hrs. 16

9/11 min (3)9hrs. 32

9/11min (4)9hrs. 16

4/11min

At what angle are the hands of a clock inclined 10 minutes past 3?

(1) 150 (2) 22

1/2

0 (3) 35

0 (4) 45

0

Ȁ Ā Ā Ā Ā Ā Ā Ā Ā Ԁ Ā Ȁ Ā Ā Ā Ā Ā Ā Ā

he angle between the hands of my watch is 1000 when the hour hand is between 7 and 8. What time

does the watch show? (1) 7hrs. 30min (2) 7 hrs. 40min (3) 7hrs. 45min (4) None of these

What time does Sushil‘s watch show when the hour hand is between 8 and 9 the angle between the two

hands of the clock is 350?

(1) 8 hrs. 45min (2) 8 hrs. 30min (3) 8 hrs. 50min (4) 8 hrs. 56min

At what time between 11 O‘clock and 12 O‘clock, will hands of a clock be at an angle of 821/2

0?

(1) 11hrs. 45min (2) 11hrs. 36min (3) 11hrs. 30min (4) 11hrs. 15min

9. Find the day of the week on March 14, 1993. (1)Monday (2) Tuesday (3) Sunday (4) Wednesday

10. Find the day of the week on April 28, 1973. (1)Friday (2) Thursday (3) Sunday (4) Saturday

11. Find the day of the week on October 31, 1984. (1) Saturday (2) Wednesday (3) Thursday (4) Monday

12. On what dates of December 1976 did Sunday fall? (1)4, 11, 18, 25 (2) 5, 12, 19, 26 (3) 6, 13, 20, 27 (4) 3, 10, 17, 24

13. Find the day of the week on Feb 12, 1992. (1)Friday (2) Thursday (3) Wednesday (4) Saturday

14. Find the day of week on 18 December 2006. (1)Monday (2) Thursday (3) Wednesday (4) Saturday

15. Find the day of week on 2 February 2024. (1)Monday (2) Thursday (3) Wednesday (4) None of these

Page | 32



Analytical Ability

Analytical Ability or Analytical reasoning based Puzzles constitute a very important part of any aptitude paper. These questions are generally asked in the form of caselets, with the data given in a few lines and some four to five questions following it which have to be answered on the basis of given facts in the caselet. An interesting fact is that these questions require practically no previous knowledge of the concepts. The only ―aptitude‖ required is to approach the question in a purely logical way. Another thing to remember is that nothing has to be assumed. Assumption is very dangerous, especially in this topic. The Puzzles or Arrangements, as they are often called, generally falls in these three categories:

TYPE I – LINEAR ARRANGEMENTS: - In these questions, the student has to arrange objects or people or books in a straight line. The information provided in the question is about the relative positions of these objects or the persons with respect to each other or with respect to the end points or the central position, etc.

TYPE II – TABULAR ARRANGEMENTS: - Here there are many variables that are related with each

through many pieces of information. The strategy to be followed here is to identify that variable which occurs most frequently in the question and make this variable as the leading row, followed by the second most frequently occurring variable becoming the second row and so on. Generally, a maximum of four to five variables are involved in a tabular arrangement question.

TYPE III – CIRCULAR ARRANGEMENTS: - In case of circular arrangements, the items or the people are

arranged in the circular fashion. Generally we have a group of about five to nine people to be arranged in a circle. So if we have an odd number of people to be arranged then none of them will be diametrically opposite to each other. Whereas in case of an even number of people to be arranged, all of them are diametrically opposite to each other.

Remember that

In linear arrangement, the arrangement by default starts from the left side and proceeds to the right side.

‗A is to the right of B‘ doesn‘t necessarily mean immediate right. We can have some people in

between A and B.

All the people in linear arrangement are to be arranged such that they are facing into the book/board,

with their backs staring at us.

If days or months are involved in the arrangement then this would obviously become the first row as their relative position is fixed.

Since a circle has no starting or an ending point, the first person can be seated anywhere on the circle.

The right of a person becomes anti-clockwise and the left of a person becomes clockwise direction.

DETERMINISTIC AND NON-DETERMINISTIC ARRANGEMENTS: -It is not another type of arrangement. Basically this distinction is made because of the sufficiency or insufficiency of the information given with the question. If the data given in the question suffices to completely determine the arrangement, then such arrangements are called deterministic arrangements. If the data given in the question is not sufficient to completely determine the arrangement, then such arrangements are called non-deterministic arrangements. Such sets are generally difficult because there are many open ends in the question. Questions in this type are usually conditional type of questions, most of the time beginning with ‗ IF ‗.

Page | 33



Questions

Data for questions 1 to 5: P, Q, R, S, T and U play volleyball, baseball, handball, chess, kho-kho and karate.

U who is heavier than Q and is lighter than T plays karate. The heaviest among play Kho-kho. P, who is between Q and R in decreasing order of weight, plays baseball. Q and R are into neither kho-kho nor chess. The lightest among them plays chess.

Who among them is the heaviest?

(1) Q (2) R (3) T (4) P (5) None of these Which sport does U play?

(1)Kho-kho (2) Volleyball (3) Baseball (4) Karate (5) None of these Who plays chess?

(1) Q (2) S (3) T (4) R (5) None of these Which sport does Q play?

(1) Handball (2) Volleyball (3) Chess (4) Baseball (5) Either handball or volleyball

Who among the following is lighter than R?

(1) P (2) S (3) U (4) Q (5) None of these

Data for questions 6 to 10: Five books G, H, I, J and K have to be proofread in 6 hours where 1 hour needs to

be given per book. A break of 1 hour has to be taken in the third or fourth hour. The proofreading cannot start with G and has to end in I. J has to immediately follow H with no break in-between. G cannot be done immediately after J. G has to precede K immediately with no break in-between.

Which hour is the break?

(1) Sixth (2) Fourth (3) Fifth (4) Second (5) Third

Which is the first book to be proofread?

(1) J (2) G (3) H (4) I (5) None of these Which book is to be proofread immediately after the break?

(1) J (2) G (3) H (4) I (5) None of these Which book is to be proofread immediately after J?

(1) H (2) K (3) I (4) G (5) None of these Which book is to be proofread immediately after K?

(1) G (2) K (3) I (4) H (5) None of these

Data for questions 11 to 15: L, M, N, O and P are students coming from Agra, Banaras, Chennai, Daman and

Egatpur. They have topped in different subjects among Eco, SP, OC, AC and BC. The student who has topped in OC is not from Agra. The student from Egatpur has topped in Eco. M comes from Daman and O from Agra. The student from Chennai has not topped in AC. L topped in AC and P in BC.

Who of the following students has topped in OC? (1) L (2) M (3) N (4) O (5) None of these

Page | 34



From which city does the topper of SP come from? (1) Agra (2) Banaras (3) Chennai (4) Daman (5) None of these

In which subject has the student from Chennai topped in?

(1) Eco (2) OC (3) BC (4) AC (5) None of these From which city does the topper of AC come from?

(1) Banaras (2) Daman (3) Egatpur (4) Agra (5) None of these From which city does N come from?

(1) Banaras (2) Chennai (3) Agra (4) Daman (5) Egatpur

Data for questions 16 to 20: A, B, N, D, E and F are members of a family in which there are 3 generations and

2 married couples. The different professions in the family are professor, Doctor, Manager, Banker, Housewife and Lawyer. E is married to A who is a professor. D who is a Housewife is the mother of A. B is the grandfather of N who is a Doctor. E who is the father of the doctor is not a Banker. F is the granddaughter of D and is a Manager.

Who among the following family members is the Banker?

(1) E (2) B (3) N (4) F (5) None of these What is the Profession of E?

(1) Manager (2) Doctor (3) Professor (4) Banker (5) Lawyer How many female members are there in the family? (1) Two (2) Three (3) Four (4) Cannot be determined (5) None of these

19. Who is the husband of the Housewife? (1) N (2) B (3) F (4) E (5) None of these

20. How is N Related to F? (1) Sister (2) Brother (3) Father (4) Cannot be determined (5) None of these

Data for questions 21 to 25: Each deodorant made by a manufacturer is a mixture of two or more components

selected from a stock of exactly five different components labelled X, Y, Z, U, and V. The manufacturer has learned that a formula for a deodorant is acceptable if and only if it does not violate any of the rule listed below.

If the deodorant contains X, it must also contain Z, and there must be twice as much Z as X. If the deodorant contains Y, it must also contain U, & the amount of U must equal the amount of Y. If Z cannot be used in combination with U.

If U cannot be used in combination with V.

If the deodorant contains V, the amount of V must be greater than the total amount of the other components used.

21. Which of the following is an acceptable formula for a deodorant?

(1) One part X, one part V (2) Two parts Y, two parts X

(3) Three parts Z, three parts X (4) Four parts U, four parts Y

22. The addition of more Z could make which of the following formulas for perfumes acceptable?

(1)One part X, one part Z, five parts V (2) Two parts X, two parts Z, two parts V (3)One part Y, one part Z, one part V (4) Two parts Y, one part Z, four parts V

Page | 35



23. Which of the following could be added to an unacceptable deodorant consisting of two parts Z and one

part V to make it acceptable? (1) One part X (2) One part Y (3) Two parts Z (4) Two parts V

24. Which of the following formulas for perfumes could be made acceptable by removing some or all of one

component? One part X, one part Y, one part Z, four parts V One part X, two parts Z, one part U, four parts V One part X, one part Y, one part U, one part V Two parts X, two parts Z, one part U, two parts V

25. Each of the following is a pair of components that can be used together in an acceptable deodorant

consisting of two or more components EXCEPT (1) X & Y (2) X & Z (3) X & V (4) Y & U

Data for questions 26 to 30: Amongst Shankar, Ehsaan and Loy, there are a professor, a fighter pilot and a

banker. They have girl friends- Deepika, Katrina and Ileana. All the three girls are working. Other information is as follows:

Loy‘s girl friend is an designer. Fighter pilot‘s girl friend is a civil servant. Shankar is cheating his girl friend by roaming around with Katrina. Deepika is courting the banker. Ileana is an expert cook.

Who is the professor?

(1) Shankar (2) Loy (3) Ehsaan (4) Ileana (5) Data insufficient

Which of the following pairs is incorrect? (1) Katrina - Civil servant (2) Ehsaan - Katrina (3) Ileana – Shankar (4) Shankar - fighter pilot (5) Deepika – Designer

28. Who is the fighter pilot? (1) Loy (2) Shankar (3) Ehsaan (4) Katrina (5) Data in sufficient

29. Who is the banker? (1) Shankar (2) Ehsaan (3) Loy (4) Deepika (5) Data insufficient

30. Who is Shankar‘s GF? (1) Ileana (2) Katrina (3) Designer (4) Deepika (5) Civil Servant

Data for questions 31 to 35: The directors of a museum are mounting an exhibition of paintings in a space

temporarily partitioned into exactly seven rooms - A, B, N, D, E, F and G. Visitors reach, room A by an elevator, and

they can enter and leave the exhibition only through room A. Once inside, visitors are free to move as they choose

from room to room. The following list includes all of the doorways that connect the seven rooms:

There is a doorway between A and B, a doorway between A and N, and a doorway between A & E. There is a doorway between B and N. There is a doorway between E and D and a doorway between E and F. There is a doorway between F and G.

After stopping to rest in G, a visitor goes from G to N, passing through no more rooms than necessary. On

reaching N, the visitor will have passed through a total of how many rooms (counting neither G nor N) since the rest stop?

(1) 2 (2) 3 (3) 4 (4) 5

If one of the doorways between two exhibition rooms is to be closed off, and yet all rooms are to remain

accessible to visitors, the closed-off doorway can be a doorway allowing passage to which of the following rooms? (1) A (2) D (3) E (4) F

Page | 36



Which of the following proposed new doorways would make it possible for a visitor to begin at A and visit

all the rest of the rooms, arriving last at G, without having entered any of the rooms in the exhibition twice? (1) A - D (2) B - G (3) N - D (4) D - F

Which of the following is a room that a visitor must enter before entering room D?

(1) B (2) N (3) E (4) F

If a visitor to the exhibition enters no room more often than necessary to visit all of the rooms and then

leaves the exhibition, which of the following rooms must the visitor enter exactly twice? (1) A (2) B (3) N (4) F

Data for questions 36 to 40: There are five houses in a row, owned by Aman, Benazir, Cinny, Daljeet, and

Emily, not necessarily in that order. Each house is of a different colour, and each of the five owners have different mobiles, and take different drinks. Benazir lives next to the blue house, while Cinny has a Nokia. The Samsung owner drinks Coca Cola and has as his neighbours the owners of Micromax and Gfive. Benazir lives in the first house from the left, while Milk is drunk in the middle house which is not the pink house. Micromax is in the yellow house, while the green house is immediately to the right of the pink house. Daljeet drinks tea, while coffee is drunk in the green house. Aman lives in the red house.

Who has orange juice for a drink?

(1) Aman (2) Benazir (3) Cinny (4)Daljeet

What brand of TV does Aman own?

(1) Samsung (2) Micromax (3) Gfive (4) Tata

In which coloured House does Emily live?

(1) Yellow (2) Blue (3) Green (4) Pink

Who drinks coffee?

(1) Aman (2) Benazir (3) Cinny (4) Daljeet

Who lives in the fourth house from left?

(1) Aman (2) Benazir (3) Cinny (4) Daljeet

Data for questions 41 to 45: L, M, N, P, Q, R, S are playing the game of truth or dare, sitting in a circle and

facing inwards. Their relative positions are as given. R is second to the right of S. M is neighbour of R but not of Q. Q, the neighbour of N, is fourth to the right of S. P is immediately between Q and L.

Who is fourth to the left of S?

(1) N (2) Q (3) P (4) Cannot be determined

Who is to the left of S?

(1) L (2) M (3) N (4) Cannot be determined

Who are the neighbours of R?

(1) L - M (2) M - N (3) N - Q (4) R - M

If the turn moves anticlockwise, who would play after M?

(1) R (2) S (3) P (4) N

If the turn moves clockwise, who would play after Q?

(1) R (2) S (3) P (4) N

Page | 37



Data Interpretation Data Interpretation is nothing but drawing conclusions and inference from a comprehensive data

presented numerically in tabular form or pictorial form by means of an illustration, graphs, pie-charts, etc. Thus the act of organizing and interpreting data to get meaningful information is data interpretation.

It is an extension of mathematical skill and accuracy and hence sound knowledge of quantitative

techniques is a prerequisite for good performance in this topic. Broadly speaking, this topic will have questions from the following categories: Tabular Data-They enable the reader to make comparisons and to draw quick conclusions. It is one of

the easiest and most accurate way of presenting data. They require much closer reading than graphs or

charts and hence are difficult and time consuming to interpret. While answering questions based on

tables, carefully read the table title and the row and column headings.

Line Graphs-This simplifies the data interpretation as it is a pictorial presentation of data and is hence

very useful for determining trends and rate of change. The slope of the line graph helps is comparing

the magnitude of change between any two consecutive points on the graph. Steeper the slope, greater is

the change ion magnitude between the two consecutive points. But remember, the slope of the graph

indicates the absolute growth and not the percentage growth.

Caselets-Here the data is given just in the form of paragraph. The student is required to understand the

data presented in the caselet and convert it into a table or equation for solving the questions.

Bar Graphs-This helps to compare the given quantities by the height or length of a bar graph. A bar

graph can have either vertical or horizontal bars. We can compare different quantities or the same

quantity at different times. In bar graphs the data is discrete. Presentation of data in this form makes

evaluation of parameters comparatively very easy.

Pie-Charts-Circle graphs or pie charts, as they are generally called, are used to show how various

sectors are related to the whole circle through angular measure. They usually give the per cent that each sector receives. In such representation the total quantity in question is distributed over a total angle of

3600.

Page | 38



Questions DIRECTIONS for questions 1 to 5: These questions are based on the following line graph.

Profit of GLASGOWE Ltd.

In R

s. L

ak

h

50 50

45 50

45

45 40

40

35

35

30 25 28

23 25

21

20 15 15

7

10

5

0

1999 2000 2001 2002 2003 2004

Profit Income Expenditure = Income–Profit

Profit

Profit percentage = Income 100

In which year is the profit percentage of Glasgowe Limited, the highest?

a) 2000 b) 2001 c) 2002 d) 2004 e) 2003

In which year is the increase/decrease in the expenditure of Glasgowe Limited, the highest

when compared to its previous year?

a) 2000 b) 2003 c) 2002 d) 2001 e) 2004

From the year 1998 to 1999, the profit of Glasgowe Limited, has increased by 40% and the income

has increased by 25%. What was the expenditure of Glasgowe Limited, in 1998?

a) Rs. 21 Lakh b) Rs. 22 Lakh c) Rs. 23 Lakh d) Rs. 24 Lakh e) Rs. 25 Lakh

The profit of Glasgowe Limited, in which year is closest to the average profit per year for the given

period?

a) 2000 b) 2002 c) 2003 d) 2004 e) 2001

In which year was the rate of change of expenditure, as compared to previous year, the highest?

a) 2001 b) 2002 c) 2003 d) 2004 e) None of these

Page | 39



DIRECTIONS for questions 6 to 10 : The following graph gives the data on the movement of the share

(stock) price of Cadbury Ltd., in the years 1999-2000 The paid-up price, at the time of public issue, was Rs. 10 per share.

The average stock price for May-September 2000 is lower than that for May-November 1999 by (in Rs.) (1) 10.90 (2) 12.65 (3) 14.85 (4) 16.20

In 1999, for the given months, the absolute variation in the share price in any month over that in the

previous month, is the highest in (1) November (2) September (3) July (4) August

From the given data, comparing the corresponding months of 1999 and 2000, in which month is the

differential in the share price the largest? (1) July (2) August (3) June (4) September

100 shares bought in September 1999, can be sold without any gain or any loss in the month of

(1) October 1999 (2) July 2000 (3) September 2000 (4) June 2000

400 shares bought in October 1999, were sold in blocks of 100 shares in November 1999, June, July and

September 2000. The loss from all the transactions is (in Rs.) (1) 1000 (2) 1500 (3) 2000 (4) 2500

DIRECTIONS for questions 11 to 15:

The following is the composition of the Student Backgrounds at a multidisciplinary college. The backgrounds

can be segregated into BE, BCOM, BA, BSC, and BBA. The BE students are one less than one-third of the

number of Bsc Students, and three less than half the number of BBA students. The number of students with

Bcom and Bsc backgrounds exceeds the number of students with BA background and BBA by 3. The number of

students with BA and Bsc backgrounds is one less than the half of the total strength. The students of BA and

BBA form 7/16th

of the total strength. The number of students with Commerce and Arts background is 29. The number of BE students is

(1) 10 (2) 7 (3) 16 (4) 28

The number of BA students is

(1) 10 (2) 15 (3) 20 (4) 25

The number of BCOM students

(1) 19 (2) 9 (3) 14 (4) 4

Page | 40



The number of BSC students is

(1) 12 (2) 16 (3) 20 (4) 24

The total strength of the students is

(1) 40 (2) 60 (3) 80 (4) 100

Question no. 16-20: - The circle-graph given here shows the spending‘s of a country on various sports during a particular year. Study the graph carefully and answer the questions given below it.

16. What per cent of total spending is spent on tennis?

(1) 12.5% (2) 22.5% (3) 25% (4) 45%

17. How much per cent more is spent on Hockey than that on Golf? (1) 27% (2) 35% (3) 37.5% (4) 75%

18.If the total amount spent on sports during the year be Rs. 1.8 crores the amount spent on Basketball exceeds

on Tennis by:

(1) 2.5 lacs (2) 3.6 lacs (3) 3.75 lacs (4) 4.1 lacs

19. How much percent less is spent on Football than that on Cricket? (1) 22.22% (2) 27% (3) 33.33% (4) 37.14%

If the total amount spent on sports during the year was Rs. 2 crores, the amount spent on Cricket and Hockey

together was:

(1) 8 lacs (2) 80 lacs (3) 120 lacs (4) 160 lacs

Page | 41



DIRECTIONS for questions 21 to 25 : Refer to the following table that gives population statistics.

South Asian Population bursting at seams

2005 2010 2015 Zero-growth size

China 1150 1300 1850 1900

India 850 1000 1350 1850

USA 250 300 350 400

Indonesia 200 250 300 350

Brazil 150 200 250 300

Japan 150 150 150 150

Nigeria 100 150 250 450

Pakistan 100 150 250 400

Bangladesh 100 150 200 250

All Figures in Millions

The combined population of India, Pakistan and Bangladesh in 2015 is less than that of China in 2015 by

(in millions) (1) 40 (2) 50 (3) 60 (4) 70

The world population in the year 2010 is 500 crores. What percent of the world population does the

combined population of India and China form? (1) 46 (2) 47 (3) 49 (4) 51

For the period 2005-2010 the country showing the highest percent, growth in population is

(1) India (2) China (3) Nigeria (4) Brazil

For Nigeria, what percent of the zero-growth population is the population in the year 2010?

(1) (2) (3) (4)

The immigrant population in the USA in the year 2015 is expected to be 100 million. The immigrant population as a percent of the total population is approximately (1) 21 (2) 23 (3) 25 (4) 29

Page | 42



Directions for 26-29:-

Study the following pie-chart and the table and answer the questions based on them.

Proportion of Population of Seven Villages in 1997

Village % Population Below Poverty Line

X 38

Y 52

Z 42

R 51

S 49

T 46

V 58

If the population of village R in 1997 is 32000, then what will be the population of village Y below poverty

line in that year? (1)14100 (2) 15600 (3) 16500 (4) 17000

The ratio of population of village T below poverty line to that of village Z below poverty line in 1997 is:

(1) 11: 23 (2) 13: 11 (3) 23: 11 (4) 11: 13 Find the population of village S if the population of village X below poverty line in 1997 is 12160.

(1) 18500 (2) 20500 (3) 22000 (4) 26000

If in 1998, the population of villages Y and V increase by 10% each and the percentage of population

below poverty line remains unchanged for all the villages, then find the population of village V below poverty line in 1998, given that the population of village Y in 1997 was 30000. (1) 11250 (2) 12760 (3) 13140 (4) 13780

Page | 43



Number System

Types of Numbers: -

Natural Numbers (N): All Counting numbers e.g. 1, 2, 3... are called natural nos.

Whole Numbers (W): All counting numbers together with zero form the set of Whole nos.

Integers (I): All natural numbers, 0 and negatives of counting numbers together form the set of integers.

Rational numbers (Q): All Numbers which can be expressed in p/q form so that (q!=0 & p,q I)

Irrational numbers (Q’): Numbers which cannot be expressed in p/q form are called as Irrational

numbers.

Subtypes of Numbers: -

Even Numbers: A number divisible by 2 is called an even number, e.g., 2, 4, 6 etc.

Odd Numbers: A number not divisible by 2 is called an odd number. e.g. 1, 3, 5 etc.

Prime Numbers: A number is called a prime number, if it has exactly two distinct factors.

Composite Numbers: If the number has more than 2 distinct factors then it is known as composite number,

e.g., 4, 6, 8, 9, 10, 12.

Co-primes: Two numbers a, b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11),

etc. are co-primes,

Perfect Numbers: If we say ‗X‘ is a perfect number then addition of all the factors of ‗X‘ (excluding X

itself) equals to the number ‗X‘. E.g. 6=1+2+3.

Divisibility Rules:-

A number is divisible by 2 when its unit's digit is even or 0.

A number is divisible by 3 when the sum of its digits is divisible by 3.

A number is divisible by 4 when the number formed by the last two digits is divisible by 4 or the last two

digits are 0.

A number is divisible by 5 when its unit's digit is 5 or 0.

A number is divisible by 6 when it is divisible by both 2 and 3.

A number is divisible by 8 when the number formed by the last three right-hand digits is divisible by 8, or

when the last three digits are 0.

A number is divisible by 9 when the sum of its digits is divisible by 9.

A number is divisible by 10 when its unit's digit is 0.

A number is divisible by 11 when the difference between the sum of the digits in the odd and the even

places is 0 or a multiple of 11.

A number is divisible by 12 when it is divisible by both 3 and 4.

Page | 44



Rules of Counting Numbers: -

Sum of first n natural numbers n

(n

1)

2

Sum of first n odd numbers n2Sum of first n even numbers n(n 1)

Sum of the squares of first n natural numbers n (n 1) (2n 1)

6

n (n 1) 2

Sum of the cubes of first n natural numbers

2

(a + b)2

= a2

+ 2ab + b2

(a – b)2

= a2

– 2ab + b2

(a + b)3

= a3

+ 3a2

b + 3ab2

+ b2

(a – b)3

= a3

– 3a2

b + 3ab2

– b3

(a + b)(a – b) = a2

– b2

(a + b)(a2

– ab + b2

) = a3

+ b3

(a – b)(a2

+ab + b2

) = a3

– b3

(a – b)2

= (a + b)2

- 4ab

(a + b)2

=(a – b)2

+ 4ab

Least Common Multiple (LCM) & Highest Common Factor (HCF): -

Highest Common Factor (HCF) of two or more numbers is the greatest number which exactly divides each of the given numbers. It is also known as GCD or GCM

Least Common Multiple (LCM) of two or more numbers is the least number which is exactly divisible by

each of the given numbers.

We can calculate HCF as well as LCM using one common method i.e. division method.

Page | 45



Questions

Which of the following groups of numbers contain only irrational numbers?

3

9

4 , 8

,

, 7, (1) (2) 4 2 8

(3) , ( 1), 3

,

3 ,

, 7

, 9

2 3

(4) 4

2

8

2

2. +3 is

(1)Rational Number (2) Irrational Number

If a & b are odd nos. then which of the following is even?

(1) a+b (2) a+b+1 (3) ab (4) ab+2

If x, y, z are odd positive integers which of the following is not necessarily true?

(1) xy + yz + zx is odd (2) x2

(y + z) is odd

(3) 3x + 5y + 2z is even (4) x2

(y2

+ z2

)/2 is odd If x, y, z are odd and distinct positive integers, which of the following cannot be true?

(1) x × y × z2 is odd (2) (x – y)

2 × z is even

(3)(x + y – z)2 × (x + y) is even (4) (x – y) × (y + z) × (x + y – z) is odd

Which of the following represents the value of 0.7121212…..?

(1) 712/990 (2) 705/990 (3) 705/999 (4) None of these

What represents 0.123333333……….

(1) 123/990 (2) 111/999 (3) 111/900 (4) 122/900

Value of X=0.a1a2 a1a2 a1a2 a1a2………… by which of the following no. we should multiply X to get an

integer?

(1) 18 (2) 108 (3) 158 (4) 198

Find a if 7a4 is divisible by 9. (1) 6 (2) 5 (3) 4 (4) 7

10. What least value must be assigned to * so that the number 451 *603 becomes exactly divisible by 9?

(1) 2 (2) 7 (3) 8 (4) 5

11. What least value must be assigned to * so that the number 63576 * 2 is divisible by 8?

(1) 1 (2) 2 (3) 3 (4) 4

12. If an integer is divisible 3 as well as 4 then it is necessarily divisible by

(1) 12 (2) 18 (3) 24 (4) 54

Page | 46



13. What will be the value of x+y if 653xy is divisible by 90

(1) 5 (2) 4 (3) 2 (4) 8

14. What is the difference between two numbers if their addition is 8 & their multiplication is 12?

(1) 6 (2) 5 (3) 2 (4) None of these

15. Find (5683-128

3)/ (568

2+568*128+128

2)

(1) 500 (2) 450 (3) 440 (4) 400

16. If addition of two nos. is 80 & their multiplication is 10 then find the addition of their reciprocal (1) 7.66 (2) 8.33 (3) 9.45 (4) 8

17. If difference of two nos. is 15 & their multiplication is 100 find addition of those two nos.

(1) 45 (2) 25 (3) 40 (4) 30

18. The sum of first 40 natural nos. is:

(1) 450 (2) 835 (3) 820 (4) 730

19. The sum of all positive even integers between 1 to 58 (including 58) is:

(1) 580 (2) 868 (3) 870 (4) 812

20. The sum of all odd natural nos. till 100 is:

(1) 2401 (2) 2500 (3) 2601 (4) None of these

21. Find a number which is less than 500 and exactly divisible by 3, 4, 5, 6, 7?

(1) 360 (2) 420 (3) 480 (4) None of these

22. Find a greatest number which is less than 1900 and divisible by 20, 25,180?

(1) 900 (2) 1350 (3) 1800 (4) 1899

23. Six lions start roaring together and roar at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30

minutes, how many times do they roar together?‘

(1) 15 (2) 16 (3) 10 (4) 5

24. Find the number which is when divided by 6, 8 & 10 leaves the same remainder i.e. 4 every time?

(1) 120 (2) 116 (3) 124 (4) 244

25. Find a number which is when divided by 6,8,10 leaves the remainder of 3, 5 & 7 respectively?

(1) 120 (2) 123 (3) 127 (4) 117

26. Find the number which exactly divides 144,240 & 576? (1) 48 (2) 42 (3) (4) 117

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27. The greatest possible length that can be used to measure exactly the lengths 10m, 15m and 30m is

(1) 5 m (2) 45 m (3) 60 m (4) 90 m

28. Find the highest number which when divides 63, 48 & 78 leaves the same remainder 3?

(1) 5 (2) 15 (3) 25 (4) None of these

A library has 120 English titles, 100 Hindi titles and 220 Regional titles. They have to be arranged in

shelves such that each shelf has titles of only kind, and each shelf has the same number of titles. How many shelves are required? (1) 25 (2) 2 (3) 22 (4) 13

30. In previous question, how many titles can be accommodated in each shelf?

(1) 23 (2) 10 (3) 46 (4) 20

In a city, there are three schools having 336, 210 and 294 students respectively. An examination

committee has to arrange a sitting arrangement for these students such that, each classroom should be occupied to the same capacity and students from same school should sit in same classroom. What is the

minimum number of classrooms needed?

(1) 42 (2) 21 (3) 20 (4) 25

32. What is the LCM & HCF of 5/12 & 7/4?

(1) 35/4, 1/12 (2) 4/35, 12 (3) 1/12, 35/4 (4) 12, 4/35

33. If LCM of two nos. is 120 & their HCF is 20 if one no. 40 then find another one:

(1) 30 (2) 25 (3) 50 (4) 60

34. How many factors does 300 have

(1) 30 (2) 25 (3) 24 (4) 18

35. How many factors does 540 have

(1) 45 (2) 20 (3) 24 (4) 18

36. How many odd factors does 120 have

(1) 16 (2) 12 (3) 4 (4) None of these

37. In the previous questions how many even factors are there?

(1) 16 (2) 12 (3) 4 (4) None of these

38. A number have total 5 factors which of the following can be the value for that no.

(1) 18 (2) 16 (3) 24 (4) 32

39. What is the unit digit of 4729

?

(1) 7 (2) 9 (3) 3 (4) 1

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40. Find the unit digit of this expression: 2345

*5619

?

(1) 3 (2) 6 (3) 9 (4) 8

41. Find the unit digit of the expression: 4734

+1460

(1) 3 (2) 6 (3) 9 (4) 5

42. What can be the unit digit for the expression: 5331

-4730

?

(1) 8 (2) 6 (3) 9 (4) None of these

43. What will be the first non-zero unit digit of the expression: 3038

(1) 8 (2) 6 (3) 9 (4) None of these

44. Find the remainder when 76 is divided by 3?

(1) 0 (2) 1 (3) 2 (4) None of these

45. What will be the remainder when 257 is divided by 6

(1) 1 (2) 2 (3) 3 (4) 4

46. Find the highest power of 2 in 100!

(1) 97 (2) 89 (3) 24 (4) 44


(1) 97 (2) 89 (3) 24 (4) 44


(1) 97 (2) 89 (3) 24 (4) 44

49. Find the total no. of zeroes at the end of 35!

(1) 5 (2) 6 (3) 7 (4) 8

50. Find highest power of 12 in 64!

(1) 28 (2) 30 (3) 31 (4) None of these

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Percentages

Finding equivalent fraction from percentages: -

To find a fraction of x% just divide x by 100. i.e. 20% is nothing but 20/100=1/5

Finding equivalent percentages from fraction: -

To find a percentages from fraction A/B just multiply it with 100, i.e. (A/B)*100 e.g.

¼= (1/4)*100=25%

Some Important formulae of Percentages: -

What is X% of Y: - (X * Y) / 100

What % of X is Y: - (Y / X) * 100

X is what % of Y: - (X / Y) * 100

% change (Increase/Decrease): - [ (Final-Initial) / Initial] * 100

Relative percentages of some fraction: -

1/1: - 100% 1/2: - 50% 1/3: - 33.33% 1/4: -25% 1/5: - 20%

1/6: - 16.66% 1/7: - 14.28% 1/8:-12.5% 1/9: - 11.11% 1/10: - 10%

1/11: - 9.09% 1/12: - 8.33% 1/13: - 7.69% 1/14: - 7.14% 1/15: - 6.66%

1/16: - 6.25% 1/20: - 5% 1/25: - 4% 1/50: - 2% 1/100: - 1%

Successive percentages change: -

If any no. is first increased by A% and it is again increased by B% then total percent change is given by the

formula a b

a

b

%

100

In case of two increments we will use A & B both positive but if one change is increment while the other is

decrement then formula will become a b

a

b

%

100

If we have three or more successive changes then take the first two changes, calculate the combined change,

now take this combined change with third one and calculate the final answer.

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Questions

Questions 1-5: Find the % equivalent of following

14/25

(1) 50% (2)53% (3) 56% (4) 60%

2. 2/7

(1) 28.56 % (2)22.22% (3) 25% (4) 7%

3. 4/9

(1) 42.56 % (2) 11.22% (3) 44.44% (4) 62.5%

4. 3/8

(1) 56.56 % (2) 42.14% (3) 37.5% (4) 62.5%

5. 1/40

(1) 4 % (2)3.33% (3) 2.5% (4) 5%

Questions 6-10: Find equivalent fractions for given Percentages

28%

(1) 3/25 (2) 7/25 (3) 14/25 (4) 25/7

7. 300%

(1) 3 (2) 1/3 (3) 30000 (4) None of these

8. 75%

(1) 3/4 (2) 2/3 (3) 3/7 (4) 4/5

9. 22.22%

(1) 22/100 (2) 2/9 (3) 3/7 (4) 4/5

10. 45%

(1) 9/10 (2) 9/20 (3) 7/15 (4) 14/15

11. 2 is what % of 50?

(1) 25% (2) 2500% (3) 4% (4) None of these

12. 1/2 is what % of 1/3

(1) 150% (2) 66.66% (3) 4% (4) None of these

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13. What % of 3/5 is 4/5?

(1) 45% (2) 75% (3) 33.33% (4) 133.33%

14. What is 55% of 400?

(1) 55 (2) 110 (3) 200 (4) 220

15. 16.66% of 600 - 33.33% of 180

(1) 100 (2) 60 (3) 160 (4) 40

Value of particular product was 6 Rs. Initially but due to inflation it becomes Rs.9 by what percent the

price got increased?

(1) 50% (2) 60% (3) 66.66% (4) 40%

Price of Samsung galaxy III was 30000$ initially but due to launch of Samsung galaxy IV it becomes

27000$ by what % price got reduced?

(1) 10% (2) 20% (3) 35% (4) 25%

85.72% of total class failed in the examination if total student passed the exam are 100 then find the

strength of class?

(1) 100 (2) 600 (3) 700 (4) None of these

19. If 50% of (X-Y) =30% of (X+Y) then what percent of X is Y?

(1) 20% (2) 400% (3) 25% (4) None of these

20. If 35% of a number is 12 less than 50% of that number, the number is:

(1) 40 (2) 50 (3) 60 (4) 80

21. Subtracting 40% of number from the number itself gives us 30 find the number

(1) 45 (2) 50 (3) 65 (4) 80

22. If 75% of number is added to 80 then the result is number itself, the number is:

(1) 320 (2) 300 (3) 35 (4) None of these

23. When we subtract 80 from a number it becomes 60% of itself find three-fourth of that number?

(1) 200 (2) 100 (3) 150 (4) None of these

24. The sum of two number is 4/3 of first number, what % of first number is second number:

(1) (1/3) % (2) 33.33% (3) 300% (4) Both 1 & 2

25. If 120 is 20% of number then find 120% of that number:

(1) 20 (2) 120 (3) 360 (4) 720

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A vendor sells 30% of his fruits and throws away 40% of the remainder. Next day he sells 50% of the

remainder and throws away the rest. What percentage of the fruits does the vendor throw? (1) 51 (2) 49 (3) 63 (4) None of these

27. What % of number from 1 to 70 have squares that end with digit 1?

(1) 1 (2) 14 (3) 20 (4) 21

28. In the market survey 20% opted for product A, 50% opted for product B & rest didn‘t buy any of them

if difference between those who opted for B & those who didn‘t buy any product is 600 then find the

no. of people for which the survey took place?

(1) 1800 (2) 3000 (3) 2000 (4) 2100

In an election between two candidates winning candidate got 55% of total valid votes while 20% votes

were invalid, if total number of vote registered were 7500 then find the number of valid votes got by

losing candidate? (1) 2500 (2) 3000 (3) 2400 (4) 2700

30. If 20% of A=B then B% of 20 is same as:

(1) 4% of A (2) 5% of A (3) 20% of A (4) 25% of A

31. If P% of P is equal to 36 then P=?

(1) 10 (2) 20 (3) 60 (4) 70

32. If X% of Y is equal to Z, what percent of Z is X?

(1) Y2/100 (2) Y/100

2 (3) 100/Y (4) 100

2/Y

33. If A is 25% more than B then by what % B is less than A?

(1) 25% (2) 20% (3) 50% (4) 75%

34. If A is 16.66% less than B then by what % B is more than A?

(1) 16.66% (2) 20% (3) 25% (4) 83.33%

35. If price of petrol is increased by 25% by what percent the consumption should be reduced so that

expenditure remains the same?

(1) 16.66% (2) 20% (3) 25% (4) 75%

If price of sugar got decreased by 28.56% then by what percent we can increase the consumption so

that expenditure remains the same?

(1) 22.22% (2) 20% (3) 60% (4) 40%

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37. A person buys some amount of sugar every month for his family but due to increase in price of sugar

by 25% he reduce the consumption by 1kg/month find his initial consumption (in kg).

(1) 4 (2) 5 (3) 8 (4) 10

38. If price of petrol becomes 75 Rs./ Lit from 60 Rs./Lit then by what percent the consumption should be

reduced so that expenditure remains the same?

(1) 16.66% (2) 20% (3) 25% (4) 75%

39. If length of rectangle got increased by 60% by what percent its breadth should be reduce so that area

remains the same?

(1) 30% (2) 37.5% (3) 50% (4) 62.5%

40. If a number is first increased by 10% and then it is again increased by 20% then what is the total

percent change?

(1) 30% (2) 37.5% (3) 32% (4) 68%

41. The price of commodity got increased by 20% because of which a family reduce the consumption by

25% what is the percent change in expenditure of family?

(1) 10% increment (2) 10% decrement (3) 5% increment (4) 5% increment

The side of rectangle is decreased by 20% & another side is decreased by 30% then by what % the area

will be changed?

(1) 56% increment (2) 56% decrement (3) 50% increment (4) None of these

43. Three successive decrement of 10%, 20% & 40% is equivalent to:

(1) 70% decrement (2) 23.2% decrement (3) 51.2% decrement (4) 56.8% decrement

44. Raman‘s salary was decreased by 50% and subsequently increased by 50%. He has a loss of…

(1) 25 % (2) 0 % (3) 2.5% (4) 0.25%

45. If side of square got increased by 10% then what is the change in area? (1) 25 % (2) 20 % (3) 21% (4) None of these

46. If radius of circle got decreased by 7% then what is the change in area? (1)14.5 % (2) 13.5 % (3) 14% (4) None of these

Page | 54



Profit Loss & Discounts

Basic Concept of CP, SP & MP: -

Cost price (CP): The price at which a person purchases an item is called the Cost Price.

Selling price (SP): The price at which a person sells an item is called the Selling Price.

Profit (P): If CP > SP, the transaction results in Profit. Thus Profit = SP-CP

Loss (L): If CP < SP, the transaction results in Loss. Thus, Loss = CP-SP

Maximum Retail Price or List Price (MRP/LP): - The price that is marked on the price tag or the price at

which the item is listed in the market is called the Marked/Listed Price. Sometimes it is also called as

the Catalogue Price.

Discount: - The difference between the MRP & SP is called as Discount.

The questions on basic concept of CP, SP & MP can be solved using only two simple concepts i.e.

Profit or Loss is always calculated on Cost Price. Discount is always calculated on Maximum Retail Price.

Dishonest Salesman: -

A dishonest salesman is a person who professes to sale his good at no profit no loss but instead of original

weight he will give you some less amount of commodity e.g. Instead of 1 kg person will give you 900

gms so he is not making the profit directly but he is making the profit indirectly and the profit earned is

given by: - [Error/Given Wt.]*100

Successive Discounts/Profit: -

Problems on successive discounts & profits can be solved in the same way as we solve the problems on

successive percent change.

Page | 55



Questions A man bought a chair for Rs.500 and sold it at 20% gain. Find its selling price.

(1)Rs. 600 (2) Rs. 550 (3) Rs. 700 (4) Rs. 650

A radio was sold for Rs.500 at a loss of 20%. Find its cost price.

(1)Rs. 600 (2) Rs. 625 (3) Rs. 700 (4) Rs. 750

A person bought an article at Rs. 200 and sold it at Rs. 250. Find his gain %.

(1)20% (2)30% (3) 25% (4) 50%

A shopkeeper buys 10 watches for Rs.2, 000 and sells them at the rate of Rs.300 per watch. Find his

gain. (1) 40% (2) 30% (3) 60% (4) 50%

Yogesh bought a scooter for Rs. 20,000. He spent 20% of his cost price towards repairs. If he wishes

to sell the scooter at Rs.30, 000, what is his gain on his overall investment? (1)50% (2) 15% (3) 25% (4) 20%

By selling an article for Rs.200, a man loses 20%. What should be the selling price of the article, if he

wants to gain 20%?

(1)Rs. 250 (2) Rs. 220 (3) Rs. 260 (4) Rs. 300

A seller sells mangoes at Rs. 44 per Kg thereby making a profit of 10%. If he makes a profit of Rs. 52,

how many Kgs of mangoes did he sell? (1) 10 Kg (2) 13 Kg (3) 17 Kg (4) 7 Kg

Tarun sells a TV for Rs. 500 and a Recorder for Rs. 270 and makes an overall profit of 10% on both. Had he sold the TV for Rs. 380 and the Recorder at its cost price, he would have lost 10%. The cost price of the Recorder is?

(1) Rs. 280 (2) Rs. 255 (3) Rs. 250 (4) Rs. 265

At what % above the cost price should be marked so that even after allowing 10% discount he should

get a gain of 20 % on the deal? (1)33.33% (2) 32% (3)30% (4) None of these

10. If 12% is allowed as discount on a radio and its selling price is Rs. 836, what is its marked price?

(1)930 (2) 940 (3) 950 (4) 960

11. If a commission of 10% is given on the list price, the gain is 20%. Find the gain percent if the

commission is increased to 20% (1)16.66% (2) 16% (3)15% (4) 6.66%

By selling 45 oranges for Rs. 80, a man loses 20%. Find the number of oranges he should sell for Rs.

48 to gain 20% in the transaction. (1) 15 (2) 16 (3) 17 (4) 18

A merchant marks his goods at Rs. 300 and allows a discount of 25%. If he still gains 12.5%, then find

the cost of article. (1) Rs. 195 (2) Rs.200 (3) Rs. 205 (4) Rs.210

Mohan buys an article with 25% discount on its marked price. He makes a profit of 10% by selling it at

Rs. 660. Find the marked price. (1) Rs. 800 (2) Rs. 825 (3) Rs. 850 (4) Rs. 875

Page | 56



15. The cost price of 21 articles is equal to the selling price of 14 articles. Find the profit. (1)25% (2)30% (3) 40% (4) 50%

16. By selling 6 dozen bananas, a shopkeeper loses the selling price of 1 dozen bananas. Find his loss.

(1)15% (2) 16% (3) 14 % (4) 16 %

17. A vendor buys lemons at 4 for one rupee and sells them at 3 for one rupee. Find his gain.

(1)25% (2) 33 % (3) 30% (4) 16 %

18. A man bought 4 lemons for a rupee. How many for a rupee must he sell to gain 100%? (1)3 (2)2 (3) 1 (4) 8

A man bought a certain number of flowers at the rate of Rs.300 for 100 flowers. 10% of the flowers were spoilt in packing. At what price should he sell the remaining so as to gain 20% on his investment?

(1)Rs. 4 (2) Rs. 3.6 (3)Rs. 3.5 (4) Rs. 3.8

20. The difference between selling an article at a gain of 10% and at a loss of 10% is Rs.136. Find the cost price of the article.

(1)Rs. 544 (2) Rs. 600 (3) Rs. 680 (4) Rs. 540

Rahul buys two BMW‘s and sells them at Rs.6, 000 each, making a profit of 20% of the cost on one and a loss of 20% of the cost on the other, what is the net result of the transaction?‘ (1)He made a gain of Rs. 500 (2) He made a loss of Rs. 500

(3)He made a gain of Rs. 1,000 (4) He made a loss of Rs. 1,000

A fraud dealer professes to sell his goods at no profit, no loss but he uses a false weight of 900gms instead of 1kg find his profit percentages? (1) 10% (2) 11.11% (3) 9.09% (4) None of these

23. A dishonest salesman professes that he sell his goods at 10% loss but he uses 800 gms weight instead of 1kg find his profit percentages?

(1) 25% (2) 17.5% (3) 15% (4) 12.5%

A shopkeeper sold rice at a profit of 20% and also uses a

weight 20% less than marked weight. Find his total gain. (1)50% (2)40% (4) 70%

If a man marks his goods 40% higher than his cost price, and allows a discount of 20%, find his net gain. (1)12%

Page | 57

(4) 28% (3) 30% (2) 20%

(3) 60%



Simple & Compound Interest

Simple Interest: -

It is the interest that is charged only on the Original sum borrowed. Hence it remains the same for all

succeeding years.

For example an interest rate of 10% per annum means on every sum of Rs. 100 lent or borrowed and extra sum of Rs. 10 will be given or taken every year.

Formula for Simple Interest (S.I) is =

100

Where, P = principal or sum being borrowed. R = Rate of interest per year. T = Time period for which the amount is borrowed. Amount = Principal + Simple Interest

Compound Interest: -

It is the interest that is calculated for each year on the amount due till that period, i.e. interest till the

preceding year is added to the principal and then the interest is calculated on this new value. The amount for a particular period becomes the principal for the succeeding period.

Calculating the compound interest can be made simple if we apply successive percent change for compound

interest.

Page | 58



Questions

Find the simple interest on Rs.2, 000 for 2 years at 12% per annum. (1) Rs. 480 (2) Rs. 400 (3) Rs.360 (4) Rs. 340

The simple interest on a certain sum at the rate of 4% for 5 years is Rs. 800. What is the sum?

(1) Rs. 2,500 (2) Rs. 3,000 (3) Rs. 3,500 (4) Rs. 4,000

The SI earned is 50 at 10% on the amount of 100 Rs. Find the time period.

(1) 2 years (2) 5 years (3)10 years (4) None of these

In how many years will the SI on Rs. 400 at 5% p.a. be the same as the SI on Rs. 600 in 4 years at 5%

p.a.? (1) 4 (2) 5 (3) 6 (4) None of these

A sum was lent out at simple interest for 3 years. Had it been lent out at 2% higher rate, it would have

fetched Rs. 60 more. Find the sum. (1) Rs. 2,000 (2) Rs. 1,000 (3) Rs. 1,500 (4) Rs. 1,700

A money lender lent equal sums of money at 6% and 4% p.a. simple interest, for a period of 3 years. If

the difference in the interest earned is Rs. 72, what is the sum lent at 4%? (1) Rs. 1,000 (2) Rs. 1,100 (3) Rs. 1,200 (4) Rs. 1,300

In what time a sum will become triple itself at 20% p.a. SI

(1) 15 years (2) 5 years (3)10 years (4) None of these

A sum becomes four times itself in 12 years, at simple interest. What is the rate of simple interest p.a.?

(1) 15% (2) 20% (3) 25% (4) 30%

At simple interest a sum doubles itself in 5 years. In how many years will it become 4 times?

(1) 10 years (2) 15 years (3) 20 years (4) 25 years

10. A certain sum of money amounts to Rs.600 in 2 years & to Rs.650 in 3 years, at SI. Find the sum.

(1) Rs. 250 (2) Rs. 500 (3) Rs. 400 (4) Rs. 300

Simple interest on a certain sum is one fourth of the sum. If the interest rate and time period are

numerically equal, find the interest rate. (1) 10% (2) 12½% (3) 5% (4) 4%

12. What is the compound interest on Rs. 4,000 for 2 years at the rate of 10% per annum?

(1) Rs. 810 (2) Rs. 840 (3) Rs. 780 (4) Rs. 880

13. Find the CI in the second year, on Rs.5, 000 at 10% p.a. (1) Rs. 500 (2) Rs. 650 (3) Rs. 550 (4) Rs. 600

14. A sum becomes 25/16 times itself in 2 years. Find the rate of CI p.a. (1) 20% (2) 25% (3) 30% (4) 12.5%

15. 64 rupees were kept on CI for 3 years which becomes 125 rupees find the rate of CI? (1) 20% (2) 25% (3) 30% (4) 12.5%

16. Find the difference between SI & CI on 700 rupees in 3 years at 10% p.a. (1) 21.7 Rs (2) 25 Rs (3) 20 Rs (4) 12.5 Rs

17. A population of country increased by 10% every year if today its 100000 after 3 years it will become? (1)130000 (2) 30000 (3) 133100 (4)33100

Page | 59



Time & Work

RELATION BETWEEN TIME, RATE AND WORK: Rate of doing work is the work done in unit time (could be days, hours, minutes etc)=

(work done)/(time taken)

Work done is the (time taken) × (rate of doing work)

Time taken to do a particular work is (work done)/(rate of doing work)

Some Important Points to remember:

If A can do a piece of work in m days he can do in one day 1/m of the work. If A can do 1/m of a work in a

day, he can complete the work in m days.

If A can do a piece of work in m days and B in n days, the ratio of the work done by A and B in same

time=n:m. Also, the Efficiency and the Wages will be in the same ratio i.e n:m

If A is twice as good a worker as B, then A will take 1/2 of the time taken by B to do a piece of work.

If the number of men doing a certain job is changed in the ratio of m:n, the time taken to complete the work

will be changed in the ratio of n:m.

If A can do a piece of work in m days, B in n days, then together they will be able to do the

work in days.

If A can do a piece of work in m days, B in n days, and C in p days, then together they will

be able to do the work in days.

If M1 people can do W1 works in D1 days working T1 hours, and M2 people can do W2 works in

D2 days working T2 hours then

CONCEPT OF CHAIN RULE-

Work and men are directly proportional to each other ie if the work increases, the number of men

required also increases and vice-versa (all other parameters assumed to remain constant).

Men and days are inversely proportional to each other ie if the number of men increases, the number

of days required to complete the same work decreases and vice-versa (all other parameters assumed to remain constant).

Work and days are directly proportional to each other ie if the work increases, the number of days

required also increases and vice-versa (all other parameters assumed to remain constant).

PIPES AND CISTERNS- A pipe or a tap connected to a tank (or a cistern or a reservoir) can do the work of

either filling it or emptying it.

If it fills the tank (or a cistern or a reservoir) then it is called an inlet.

If it empties the tank (or a cistern or a reservoir) then it is called an outlet.

Thus in Pipes and Cisterns, a filling pipe or tap does positive work and an emptying pipe or a leak does

negative work.

Page | 60



Questions

If A can do a particular job in 10 days while B can do the same job in 15 days, in how many days the job will be completed if A & B are working together? (1)12.5 Days (2)7.5 days (3)6 days (4) None of these

P and Q can do a work in 18 days. If P alone can do the work in 30 days, how many days will Q take to

complete the work? (1) 40 days (2)45 days (3)60 days (4)42 days

P can do a work in 20 days, Q can do it in 30 days and R can do it in 24 days. In how many days can they,

together, complete the work? (1) 10 days (2)4 days (3)6 days (4)8 days

A and B can do a job in 25 days and 20 days, respectively. A started the work and was joined by B

after 16 days. The number of days taken to complete the work is

(1) 15 days (2)12.2 days (3)16 days (4)16.66 days

A and B can do a piece of work in 24 days. After they have worked together for 15 days, B leaves and A

completes the remaining work in 15 days. In how many days can B alone do the work? (1) 40 days (2)60 days (3)75 days (4)80 days

A and B together can do a work in 10 days, while B and C can do it in 15 days. After A worked at it

for 3 days and B for 6 days, C finished it in 18 days. In how many days can C alone complete the work? (1) 15 days (2) 30 days (3) 25 days (4) 18 days

A can do the job in 10 days B can do the same in 15 days, with the help of C they can do it in 5 days if they

get 600 rupees for the job find the share of A? (1) 300 (2) 200 (3) 100 (4) None of these

R can do the job in 8 hrs while R & S together can do it in 12 hrs if they get 200 rupees for the job find the

share of B? (1) 30 (2) 80 (3) 120 (4) 160


A & B together can do the job in 12 days; B & C together can do the same in 15 days and C & A can do it in 20 days.

In how many days A, B & C together will do the same job? (1) 12 days (2) 8 days (3) 10 days (4) None of these

10. In how many days A alone will do the same job? (1) 30 days (2) 20 days (3) 60 days (4) None of these

11. In how many days B alone will do the same job? (1) 30 days (2) 20 days (3) 60 days (4) None of these

12. In how many days C alone will do the same job? (1) 30 days (2) 20 days (3) 60 days (4) None of these

13. If they got 720 rupees for the job find the share of B. (1) 360 (2) 120 (3) 240 (4) None of these

14. If they got 900 rupees for the same job find the share of C. (1) 300 (2) 150 (3) 200 (4) None of these

A can do a job in 10 days where as B can do it in 30 days. If they work together on alternate days, with A

starting fist, find in how many days the work will be completed? (1)14 days (2)14.33 days (3)14.66 days (4) 15 days

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Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How

many turns will it take if buckets P and Q are used alternately, to full an empty drum? (1) 30 (2) 40 (3) 45 (4) 90

Geeta and Sita, working separately, can mow a field in 8 and 12 hours respectively, if they work in

stretches of one hour alternately, Geeta beginning at 9 a.m., when will the mowing be finished? (1) 6 p.m. (2) 7 p.m. (3) 5 p.m. (4) 6.30 p.m.

A, B and C can do a job in 11, 20 and 55 days respectively. On the first day A is assisted by B and on

the second day by C. How soon can the work be completed if A is assisted by B and C on alternate clays? (1) 7 days (2) 9 days (3) 8 days (4) 10 days

19. If A is twice as good workman as B and working together they can finish the whole job in 14 days in how many days A alone will finish the job? (1) 7 days (2) 21 days (3) 42 days (4) None of these

A is twice as good a workman as B and is therefore able to finish a price of work in 20 fewer days than

B. In how many days A can finish the job (1) 15 days (2) 20 days (3) 40 days (4) None of these

A is twice as good a workman as B and is therefore able to finish a price of work in 20 fewer days than

B. Find the time in which they can do it, working together. (1) 12.5 days (2)15.5 days (3) 13.33 days (4) 14.33 days

22. A & B together can do the job in X days if A can do it in X+16 days and B can do it in X+9 days find the value of X? (1)12 days (2) 9 days (3) 8 days (4) 10 days

Two pipes A and B fill a tank in 20 minutes and 30 minutes respectively and pipe C will empty tank in

60 minutes. If all three are open, how much time will it take to fill an empty tank? (1) 12 min (2) 15 min (3) 20 min (4) 25 min

24. A water tank is filled up by a tap in 6 hours and emptied by a drain in 9 hours. If both are kept open, how long will it take to fill up completely a half-filled tank?

(1)18 hours (2) 6.2 hours (3) 9 hours (4) 12.4 hours

Pipes A and B can fill a tank in 30 & 45 min respectively. To fill the half tank only pipe A is open and

for the other half both pipes A and B are open, what is the total time taken to fill up the tank? (1) 18 min (2) 19.5 min (3) 22.5 min (4) 24min

26. A pipe A can fill a tank in 30 minutes while pipes A and B together can fill the tank in 20 minutes. If pipe B can pump 6 liters of water in one minute, find the capacity of the tank.

(1) 6 liters (2) 360 liters (3) 1,200 liters (4) none of these

Pipes A, B and C can fill a tank in 12 minutes, 36 minutes and 18 minutes respectively. If all time pipes

are open, then after what time C must be closed so that the tank is full in 8 minutes? (1) 2 min (2) 5 min (3) 3 min (4) 4 min

28. 12 men do a work in 20 days. In how days can 1 man do the job? (1) 120 (2) 200 (3) 240 (4) 300

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29. 10 Men can do a work in 12 days. To complete the work in 8 days, how many more men are required?

(1) 15 men (2) 5 men (3) 10 men (4) 12 men

30. A garrison of 200 men has provisions for 10 days. If 50 more men join, for how many days will the

food last?

(1) 8 (2) 9 (3) 6 (4) 7

8 men complete one third of the work in 5 days. How many more men should be employed to finish the

rest of work in 4 days? (1) 10 (2) 8 (3) 16 (4) 12

32. 15 workers are scheduled to complete a job in 24 hours. After 10 hours, the supervisor decides to

complete the remaining work in the next 10 hours. How many additional workers are required? (1) 3 (2) 4 (3) 5 (4) 6

A work is to be completed by 10 men in 12 days. After 8 days only one fifth of the work is completed.

How many more men are to be employed so that the work may be completed in time? (1) 40 men (2)50 men (3) 60 men (4) 70 men

6 Engineers can build a computer server in 10 hrs, they started the work at 11am and they worked till 5 pm after that one engineer joins them every hour at what time the server will be built? (1) 7.45pm (2) 8.30pm (3) 7pm (4) 8pm

A man started working alone on first day, from the second day onwards one man joins him daily till the

work is finished, working in this way they complete the whole work in 20 days, now instead of this group if 7 men works continuously to finish this task, in how many days they will finish this task?

(1) 25 (2) 27 (3) 28 (4) 30

36. If 10 men can complete a particular job in 8 days working 3 hrs per day, in how many days 15 men can do twice the work if they are working 4 hrs per day? (1) 2 (2) 4 (3) 6 (4) 8

37. If 2 men or 3 women can complete a job in 10 days in how many days 8 men & 3 women can complete

the same job? (1) 2 (2) 3 (3) 4 (4) 5

If 10 men can do a particular job in 15 days while 15 women can do the same job in 20 days in how

many days 20 men & 10 women can complete the same job? (1) 20 (2) 10 (3) 6 (4) 8

12 men or 15 women can do a particular job in 4 days. 6 men started working on the job and after

working for 2 days all of them stopped working. How many women should be put on the job to

complete the remaining work so that it gets completed in 3 days? (1) 20 (2) 15 (3) 18 (4)22

2 men and 3 boys can do a work in 8 days. The same work can be done by 3 men and 2 boys in 7 days.

How long will it take 5 men and 4 boys to do the work? (1) 9 days (2) 6 days (3) 8 days (4) 4 days

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Time Speed & Distance

Relation between Time, Speed & Distance: -

The relation between time speed and distance can be given by three basic formulae.

Time = Distance Speed = Distance Distance=Speed* Time

Speed

Time

Conversion of units of speed: -

There are two basic units of speed which are Meter per second i.e. denoted by (m/s) & Kilometer per hours

i.e. denoted by (kmph) or (km/h).

For conversion of kmph to m/s

multiply it by 5/18.

For conversion of m/s to kmph

multiply it by 18/5. Average Speed: -

If a person is moving from A to B with the speed of “X” kmph & from B to A with the speed of ―Y”

kmph then average speed can be given by (2*X*Y) / (X+Y).

If person is moving from A to B with the speed of “X” kmph & he covers a distance from B to C in same

time with “Y” kmph then the average speed is (X+Y) / 2.

Generally Average Speed is ratio of Total Distance Covered to Total Time Taken

Relative Speed: -

Two objects moving in opposite Direction: - If two objects are moving in opposite direction then

two cases are possible either they are coming towards each other or they are going away from each

other. In any of these two cases speeds of the two objects will be added to find the relative speed.

Two objects moving in same direction: - If two objects are moving in same direction then only

one case is possible i.e. second object is chasing the first object.

In both the possible ways of relative speed, the distance covered is relative distance in relative

time and relative speed is applicable if and only if the time of moving is same.

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Trains: -

Train passing a stationary object of negligible length: - If Train is passing an object of negligible length it will cover the distance which is equal to length of train itself. So Time taken to pass an object of negligible length is: L

S

Train passing a stationary object of considerable length: - If Train is passing an object ofconsiderable length i.e. bridge or platform then the total distance to be covered will be length of train &

length of the object, so time taken to pass an object of considerable length is: L1+L2 S

Train passing a moving object of negligible length: - If train is passing an object of negligible lengthbut if it is moving with the speed of S2 then time taken to pass that object will be L

S1+S2

Train passing a moving object of Considerable length: - If train is passing an object of considerablelength and it is moving with the speed of S2 then time taken to pass that object will be L1+L2

S1+S2 Boats & Streams: -

Downstream motion of a boat is its motion in the same direction as the flow of the river.

Upstream motion of a boat is its motion in the opposite direction as the flow of the river.

There are two parameters in these problems.

Speed of the stream or river (R): This is the speed with which the river flows.

Speed of the boat in still water (B): If the river is still, this is the speed at which the boat would be moving.

The effective speed of a boat while moving upstream = B - R

The effective speed of a boat while moving downstream = B + R

The speed of the boat in still water is given as B = 21

(d + u) and the speed of the river R

21

(d - u), Where, d and u are the downstream and upstream speeds, respectively.

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Questions A car travelling with a speed of 40 kmph covers the distance between A and B in 3 hours. A person

starts from B, With a speed of 20 kmph. How much time will he take to reach A? (1)5 hours (2)6 hours (3) 4 hours (4) None of these

Two persons M and N started from Bangalore to Chennai. Their speeds are in the ratio 4:5. If M takes

7 hours more than N to reach Chennai, find the time taken by N to reach Chennai. (1)28 hours (2)35 hours (3) 63 hours (4) None of these

Sunil goes to college with a speed of 10 kmph and returns to the house with a speed of 20 kmph. If he

takes 3 hours in all, find the distance between the college and house. (1)10 km (2)15 km (3) 20 km (4) 18 km

Walking at 7/8th

of his usual speed, a person is late to his, office by 15 minutes. Find his usual time to reach the office.

(1)63 min (2)91 min (3)105 min (4) 77 min

If a boy walks from his house at 4 km/hr, he reaches school 10 min early. If he walks at 3 km/hr, he

reaches 10 min late. What is the distance from his house to school?

(1) 2 km (2) 4 km (3) 8 km (4) 16 km

Travelling at his usual speed a car covered 120 km. Had he travelled at 10 kmph faster he would have covered 40 km more than it actually did in the same duration of time. Find its usual speed. (1)20 kmph (2)25 kmph (3)30 kmph (4)35 kmph

Two men A and B walk from P to Q, a distance of 21 km, at 3 and 4 km an hour respectively. B reaches Q, returns immediately and meets A at R. Find the distance from P to R. (1) 18 km (2) 12 km (3) 16 km (4) 21 km

Excluding stoppages, the speed of a bus is 54 km/hr and including stoppage, it is 45 km/hr. For how

long does the bus stop per hour?

(1) 20 min (2) 12 min (3) 15 min (4) 10 min

A man walks at the rate of 5 kmph. After every km he rests for 5 minutes. How long does it take him to travel 6 km? (1)72 min (2)102 min (3) 67 min (4) 97 min

10. A boy went from his house to school with the speed of 20kmph & returns back with the speed of

30kmph for the whole journey find the average speed?

(1) 25 km (2) 12 km (3) 24 km (4) 21 km

An athlete runs three successive 1 km stretches at speeds of 10, 15, and 20 kmph respectively. Find his average speed over entire distance. (1)14 kmph (2)12 kmph (3) 13.2 kmph (4) 13.8 kmph

12. Two cities P and Q are 110 km apart. Person A started from city P at 7 a.m. at 20 km/hr and B started

from city Q at 8 a.m. at 25 km/ hr. At what time will they meet?

(1) 10 am (2) 11 am (3) 1pm (4)12 noon.

A thief sights a policeman 50 m ahead of him. He immediately turns back and starts running at 4 kmph.

The policeman chases him at a speed of 5 kmph. After what time does the police man catch the thief?

(1)4 min (2)4 min 40 sec (3) 3 min (4) 3 min 50 sec

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Two Trucks start at the same time from Aligarh and Delhi and proceed towards each other at 36 kmph

and 42 kmph respectively. When they meet, it is found that one truck has traveled 48 km more than the

other. Find the distance between the two stations (in km) (1) 630 km (2) 624 km (3) 620 km (4) 650 km

The distance between A and B is 15 km. Salman starts from A and Katrina starts from B at speeds 30 kmph and 20 kmph respectively and travels towards each other. At what distance from A will they meet? (1)5 km (2)15 km (3) 9 km (4) 10 km

The driver of a car sees a bus 40 m ahead of him. After 20 s, the bus is 60 m behind. If the speed of the

car is 30 km/hr, what is the speed of the bus? (1) 6 km/hr (2) 12 km/hr (3) 9 km/hr (4) 24 km/hr

A car and a bus are 120 km away from each other speed of both car and bus is 60 kmph they started coming towards each other, at the same time a bird started with car towards bus with the speed of 120kmph he touches the top of the bus and immediately returns back towards the car he continues this process till the bus and car meets each other how much distance does it covers?

(1)60 kmph (2) 90 kmph (3) 120 kmph (4) 180 kmph

18. Find the time taken by a train 150 m long running at 90 kmph to cross an electric pole. (1)7 sec (2)8 sec (3) 6 sec (4) 5 sec

19. A train 100 meters long passes a platform of 500 m in 30 seconds. Find the speed of the train. (1)54 kmph (2) 90 kmph (3) 36 kmph (4) 72 kmph

A train passes an electric pole in 5 seconds and a platform 150 m long in 20 seconds. Find the speed of

the train. (1)36 kmph (2)18 kmph (3) 25 kmph (4) 50 kmph

A train 700 m long is running at a speed of 72 km/hr. If it crosses a tunnel in 60 sec, then find the

length of the tunnel (in meters). (1) 400 m (2) 450 m (3) 475 m (4) 500 m

22. A man sees a train passing over a bridge 1 km long. The length of the train is half that of the bridge. If the train clears the bridge in 2 min, the speed of the train is

(1) 45 km/hr (2) 60 km/hr (3) 30 km/hr (4) 90 km/hr

A train 270 m long is moving at a speed of 25 kmph. It will cross a man coming from the opposite

direction at a speed of 2 kmph in what time. (1) 36 sec. (2) 40 sec. (3) 44 sec. (4) 48 sec.

Two trains whose lengths are 180 m and 220 m respectively are running in direction opposite to one

another. If their velocities are 40 kmph and 50 kmph, Find time taken by them to cross each other (1) 16 sec (2) 18 sec (3) 20 sec (4) 22 sec

25. Two trains are running on parallel tracks and in the same direction at speeds of 90 kmph and 54 kmph. The faster train passes the slower train in 20 seconds. Find the total length of the trains. (1)50 (2)200 m (3) 100 m (4) 150 m

26. Two trains travel in opposite directions at 36 km/hr and 45 km/hr respectively. A man sitting in the slower train passes the faster train in 8 s. The length of the faster train is (1) 180m (2) 150 m (3) 210 m (4) 175 m

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The lengths of two trains are 120 m and 80 m long. If they are moving in the same direction, the faster train

takes 40 seconds to completely pass the slower. If they are moving in opposite directions, they completely pass each other in 10 seconds. Find their speeds. (1)45 kmph, 27 kmph (2) 45 kmph, 28 kmph (3)47mph, 25 kmph (4) None of these

28. The speed of a boat upstream and downstream is 10 kmph and 18 kmph respectively. Find its speed in still water. (1)7 kmph (2)14 kmph (3) 4 kmph (4) 8 kmph

A man can row along the stream at 24 kmph and against the stream at 16 kmph. Find the speed of the

stream. (1)5 kmph (2)4 kmph (3) 6 kmph (4) 7 kmph

A man can row downstream at 12 kmph. The speed of the stream is 5 kmph. Find the speed of rower

upstream. (1) 2 kmph (2)1 kmph (3) 1.5 kmph (4) 3 kmph

31. A man can row 18 km downstream in 3 hours and 15 km upstream in 5 hours. Find the speed of

stream. (1)1.5 kmph (2)3 kmph (3) 6 kmph (4) 4.5 kmph

A boat travels from A to B and comes back in 5 hours. If the speed of the boat in still water is 5 kmph and

the speed of the current is 1 kmph, find the distance between A and B. (1)10 km (2)12 km (3) 11 km (4) 9 km

A man rows a distance downstream in 45 min and the same distance upstream in 75 min. What is the ratio

of speed of the stream to the boat in still water? (1) 1: 4 (2) 3: 5 (3) 5: 3 (4) 4:1

34. A man can row at 6 km/hr in still water & a river is flowing at 4 km/hr. How long will the man take to

go to a place 1 km downstream & return? (1) 36 minutes (2) 24 minutes (3) 12 minutes (4) 18 minutes

A man can row at 12 km/hr in still water. He finds that it takes him thrice as much time to row up the river

as it takes to row down the river. What is the speed of the current? (1) 6 km/hr (2) 24 km/hr (3) 48 km/hr (4) 18 km/hr

Questions 36-38: - Bhim and Arjun were exercising during their Vanvaas. They start running on a circular track

simultaneously and in the same direction. If Bhim takes 4 min to complete one full round, and Arjun takes 7 min to complete one full round.

36. After how much time will they meet for the first time?

(1) 9 min. 40 secs. (2) 9 min. 10 secs. (3) 9 min. 30 secs. (4) 9 min. 20 secs.

37. After how much time they will meet on the starting point for the first time? (1) 28min (2) 18 min 40 sec (3) 9 min.20 sec (4) None of these

38. On how many different points they will meet on circular track? (1) 2 (2)1 (3) Infinite (4) 3

An athlete is running around a circular track. He takes 60 seconds for one complete round around the track.

This athlete keeps meeting another athlete, running in the opposite direction, every 15 seconds. How long does the second athlete take for one complete round around the track? (1) 20sec (2)15 sec (3) 30 sec (4) 60 sec

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Ratio Proportion Variation & Partnership

Simple Ratio & Compound Ratio: -

Comparison of any two quantities which are having the same unit is known as ratio.

Any ratio of the form A: B is called as simple ratio.

A ratio of three or more numbers is known as compound ratio e.g. A: B: C

To solve the questions based on ratios first of all assume the numbers as multiple of any natural no. X e.g. if

A: B=3: 5 so consider A=3x & B=5x and then solve the question.

Proportion: -

When two ratios are equal, the four quantities composing them are said to be proportional.

In terms of the notations, if A

C

then A, B, C and D are proportional.B D

We use the symbol "::" to express it mathematically. So whenever we write A: B:: C: D, it is interpreted as A, B, C and D are proportional.

The terms A and D are called the extremes and the terms B and C are called the means. It is very easy to note that A x D = B x C.

This result is more commonly expressed as: "Product of the extremes = Product of the means".

Continued Proportion: a, b, c, d, e, f...are said to be in continued proportion if a

b

c

d

e

...

b c d e f

When three quantities a, b and c are in continued proportion then b is called the mean proportional and c is called the third proportional.

Types of Proportions: -

Direct Proportion: Let there be two variables A and B. They are said to be in direct proportion if the ratio A: B is constant for all the possible values of A and (the corresponding values of) B. We can understand this in terms of percentages also: Two quantities A and B are in direct proportion if change in the value of A, by a certain percentage, always corresponds to the same percentage change in the value of B. Direct Proportion is characterized by the following equation:

A K , a constant

B

Note: That B

1 , again a constant. When A is in a direct proportion to B then B is in a direct

A K proportion to A as well.

Inverse Proportion: Two variables A and B are said to be in inverse proportion if the product A B is

constant for all the possible values of A and (the corresponding values of) B. We can understand this in terms of percentages also: Two quantities A and B are in inverse proportion if increase/decrease in the

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value of A, by a certain percentage, always corresponds to the same percentage decrease/increase in the value of B. Inverse Proportion is characterized by the following equation: A B = K, a constant

Note: That when A is in inverse proportion to B then B is in inverse proportion to A as well.

Partnerships: -

When two or more persons invest money in a common business, they are called partners and the business relation is called partnership.

In a partnership business, every partner invests two entities.

Time Money

It follows quite easily that different partners may invest different amounts of money. What may not follow that easily is that even the time for which the money is invested by the partners could be different. Now what is meant by that? It only means that partners join the business at different points of time.

For example consider a business in which A, B and C are partners. Suppose A and B invested amounts a

and b at the start of the business. Three months after that, C joined as a partner investing an amount c. At the end of the first year A and B invest their respective amounts for one full year but C has invested his amount for 9 months only. Hence, it follows that a partner's Investment is a product of the time and the money:

Investment = Time Money. How to share a Profit (or a Loss)?

The total profit or loss is distributed among the different partners in direct proportion of their investments. So if

three partners A, B and C have invested amounts a, b and c for time periods tA,tB and a : tB b : tC c

It follows that if tA= tB = tC then PA : PB : PC :: a : b : c

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Questions If Rs. 750 is divided in the ratio of 3:2, what is the larger part?

(1)Rs. 450 (2) Rs. 250 (3) Rs. 350 (4) Rs. 300

A certain amount of money is divided among A, B and C in the ratio 3:5:2. If B got Rs. 300 more than

C, find the amount. (1)Rs. 1,500 (2) Rs. 1,000 (3) Rs. 2,000 (4) Rs. 4,000

Rs. 1,000 is divided among A, B and C such that B's share is one third of what A and C get together.

Find B‘s share. (1)Rs. 250 (2) Rs. 300 (3) Rs. 400 (4) Rs. 550

The ratio of the father‘s age to the son‘s age is 4:1. The product of their ages is 196. What will be the

ratio of their ages after 5 years?

(1) 4:1 (2) 3:2 (3) 11:4 (4) 5:3

The ratio of fares of trains A, B and C between two cities is 2:4:5. If the fare of each train is increased

by Rs. 500 the ratio changes to 3:5:6. Find the fare of train C before increase. (1)Rs. 1,000 (2) Rs. 2,000 (3) Rs. 2,500 (4) Rs. 3,000

The ratio between two numbers is 2:3 and their LCM is 60. Find the first number.

(1)15 (2) 20 (3) 40 (4) 10

The ratio of the first and second class fares between two stations is 4:1 and that of the number

passengers travelling by first and second class is 1:50. If Rs. 2,700 is collected as fare, find the amount collected from second class passengers. (1)Rs. 2,500 (2) Rs. 2,000 (3) Rs. 2,200 (4) Rs. 2,100

A box containing a dozen ceramic mugs is dropped. Some of the mugs broke. Which of the following

cannot be the ratio of broken and unbroken mugs?

(1) 2: 1 (2) 5: 7 (3) 7: 5 (4) 3: 2

If a:b=3:5 and b:c = 2:1, find a:b:c. (1)3:10:1 (2) 6:10:1 (3) 6:10:5 (4) 6:5:1

The ratio of A's money to that of B's money is 4: 5 and B's money to C's money is 2: 3. If A has Rs.

800, then total amount of money among A, B and C is: (1) Rs. 2,790 (2) Rs. 3,300 (3) Rs. 3,000 (4) Rs. 3,620

The expenses of an institute are partly constant and partly vary as the number of employees. When

there are 20 employees, the expenditure is Rs. 1, 80,000. When there are 30 employees, the expenditure is Rs. 2, 60,000. Find the expenditure when the number of employees is 35. (1)Rs. 3, 20,000 (2) Rs. 3, 00,000 (3) Rs. 3, 40,000 (4) None of these

Present ages of Dilip & Rahul are in the ratio 5:4 respectively. Three year hence the ratio of their ages

will become 11:9 respectively what is Rahul‘s present age in years? (1)24 (2) 27 (3) 40 (4) 10

A man is 24 years older than his daughter‘s age, his age will be in the ratio of 2:1 with his daughters

age in 2 years from now find his daughters present age? (1)24 (2) 20 (3) 22 (4) 18

Six years ago, the ratio of the ages of Kunal and Sagar was 6: 5. Four years hence, the ratio of their

ages will be 11: 10. What is Sagar's age at present? (1)16 (2) 18 (3) 20 (4) None of these

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15. The sum of the present ages of father and his son is 60 years. Six years ago father‘s age was five times

the age of the son. After 6 years sons age will be:

(1)12 (2) 14 (3) 18 (4) 20

Rs. 3,960 is divided among A, B and C such that half of A's part, one third of B's part and one sixth

of C's part are equal. Then B's part is (1) Rs. 1,080 (2) Rs. 960 (3) Rs. 1,720 (4) Rs. 1,540

17. If 4x=3y=2z,then x:y:z is (1) 4:3:2 (2)2:3:4 (3) 3: 4: 2 (4) 3: 4: 6

18. Find the highest ratio amongst: (1) 5/7 (2)9/10 (3)19/22 (4) All are same

19. Find the lowest ratio amongst: (1) 5/7 (2)9/10 (3)19/22 (4) All are same

20. Find the fourth proportional 1, 2 and 3. (1)4 (2) 5 (3) 6 (4) 7

21. Find the mean proportional between 16 and 25. (1)400 (2) 20 (3) 10 (4) 40

22. Mean proportional between 8 and 72 is (1) 24 (2) 40 (3) 16 (4) 32

23. Find the third proportional of 20 & 30 (1) 45 (2) 40 (3) 30 (4) 32

P, Q and R entered into a partnership with investments of Rs. 20,000 Rs. 30,000 and Rs. 40,000 respectively. At the end of the year, Q got Rs. 3,000 as his share of the profits. Find the total profit of the business. (1)Rs. 10,000 (2) Rs. 8,000 (3) Rs. 7,000 (4) Rs. 9,000

Ratna and Giri started a business. Ratna invested a capital of Rs. 50,000. At the end of year, total profit

of the business is Rs. 10,000 and Ratna got Rs. 8,000 as his share. Find the investment of Giri. (1)Rs.10,000 (2) Rs. 20,000 (3) Rs. 30,000 (4) Rs. 12,500

A & B together started a firm by investing Rs. 50,000 and Rs. 80,000. Four months later, C joined by

investing Rs. 60,000 and B left the firm. If the total profit is Rs. 35,000 at the end of year, find the

profit share of B. (1) Rs. 8,000 (2) Rs. 7,000 (3) Rs. 5,000 (4) Rs. 9,000

Shankar started a business with a capital of Rs. 15,000. Two months later, Ehsaan joined by investing

Rs. 20,000. After two months Loy also joined in the business with a capital of Rs. 30,000. At the end of year, they got Rs. 3,100 as total profit. Find the share of Shankar. (1)Rs. 900 (2) Rs. 800 (3) Rs. 1,200 (4) Rs. 1,000

28. A, B and C enter into a partnership with A investing Rs.3,000 for the whole year, B investing Rs. 2,000

initially and increasing it to Rs.3,000 at the end of 4 months, while C invests Rs. 2,000 initially but withdraws Rs. 1,000 at the end of 8 months. What is A‘s share in profit at the end of the year, if the total profit is Rs. 2,200?

(1)Rs. 800 (2) Rs. 500 (3) Rs. 300 (4) Rs. 900

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Averages Mixtures & Allegation

Averages: -

The average (also called mean or arithmetic mean) of a number of quantities of the same kind is given by

their sum divided by their number.

Thus, Average of n quantities = (Sum of n quantities)/n

From above, Sum of n quantities = Average x n

Note: The following can serve as some shortcut tips to solve few questions.

If the given quantities are all same then average is the same value.

If the given quantities are not same then average is always greater than the smallest quantity and always less than the largest quantity.

The average of first ‗n‘ natural numbers is (n + 1)/2.

The average of ‗n‘ successive numbers is the middle term if n is odd or it is the average of the

2 middle terms if n is even.

The above formula technique also works if instead of successive numbers, we are given

numbers in an A.P.

If all the given numbers in a set are multiplied by n, then their average is also multiplied by n to give An.

If all the given numbers in a set are increased/decreased by n, then their average is also

increased/decreased by n to give A+/- n.

Weighted average (combined average):-

If w1 and w2 quantities have averages A1 and A2 respectively, then the weighted average is

given

Weighted Average = (A1 w1 + A2 w2) / (w1+w2).

The quantities w1 and w2 are called weights of A1 and A2 respectively, as the bigger of these

two quantities will decide the proximity of the net average towards the given averages A1 andA2.

Alligation method:-

This is a method where A1 and A2 are written in a horizontal line, slightly separated from each other and

Aavg is written slightly lower between them. Then the absolute differences A1 – Aavg is written

diagonally across and Aavg – A2 is written again diagonally across. The ratio of Aavg – A2 : A1 – Aavg is

also the ratio of the weights w1 : w2.

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Thus w1 : w2 = Aavg – A2 : A1 – Aavg . Simplification of this formula again gives the weighted average

formula.

Concentration/dilution of mixtures and solutions:-

If a solution or mixture contains two liquids X and Y, the presence of the liquids X and Y is expressed in

terms of percentage concentration. The concentration of X is expressed as X/(X+Y) × 100%. Similarly,

the concentration of liquid y in the mixture is [Y/(X+Y)] × 100%.

Applications of alligation method:-

The Alligation method is very frequently used in the following types of questions- To obtain A1, A2 or Aavg. To obtain the ratio w1:w2, or to find either w1 or w2. When one constituent of mixture/solution is pure milk (or pure water).

Replacement of part of solution with pure solution:-

If a container contains x units of liquid and y units of the liquid is replaced by another liquid for n times,

then the amount of the first liquid left in the can = x[1–(y/x)]n

units. In other words,

Final proportion = Initial proportion × (1 – fraction removed)n

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Questions Find the average of 20, 40 and 60.

(1)10 (2) 20 (3) 30 (4) 40

The average of 4 numbers is 16. Find the sum of the numbers.

(1) 20 (2) 24 (3) 64 (4) 54

Find the average of first four multiples of 8.

(1)21 (2)24 (3) 8 (4) 32

The average of first 5 multiples of a number is 15. Find the number.

(1)5 (2)4 (3) 3 (4) 2

The average of 4 numbers is 11. If each number is multiplied by 2, find the average of new set of

numbers. (1)32 (2)22 (3) 15 (4) 20

The average score of a batsman in 6 matches is 75 and that of the first five is 80. Find his score in the

sixth match. (1)100 (2)50 (3) 30 (4) 20

A batsman scored 135 runs in his 20th

innings and increased his average by 5 runs. What is his

average after 20 innings?

(1)35 (2)30 (3) 45 (4) 40

In the first 10 overs of a match. The run rate was only 3.2 runs per over. What should be the run-rate in

the remaining 40 overs to reach the target of 282 runs? (1)6.25 (2) 6.15 (3) 7.25 (4) 8.50

The average age of a class of 15 students is 20 years. If teacher‘s age be included, the average age

increases by 1 year. Find the age of teacher. (1)40 years (2) 36 years (3) 42 years (4) 41 years

10. Find the average of first 50 natural nos. (1)50 (2)51 (3)25 (4)25.5

11. Find the average of first 50 even nos. (1)50 (2)51 (3)25 (4)25.5

12. Find the average of first 50 odd nos. (1)50 (2)51 (3)25 (4)25.5

13. Find the average of all the natural numbers till 100 which are multiples of 7

(1)51 (2)52 (3)52.5 (4)49

14. If average of 87, 93, X, 91 is 89 then find the value of X. (1)89 (2)85 (3)92 (4)90

The average age of the family of four persons is 24 years. If the youngest member is 3 years old, find

the average age of the family at the birth of the youngest member. (1)31 years (2) 28 years (3) 27 years (4) 21 years

The average age of A, B, C, D four years ago was 51 years. If E is included, their present average age

will be 52 years. Find the present age of E. (1)35 years (2) 40 years (3) 45 years (4) 50 years

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17. There are 30 students in a hostel. If the number of students is increased by 10, the expenses of the mess

increase by Rs.100 per day, while the average expenditure per head would reduce by Rs.5. Find the original expenditure of the mess per day.

(1)Rs. 1,000 (2) Rs. 700 (3) Rs. 900 (4) Rs. 500

The average weight of three men A, B and C is 70 kg. Another man D joins the group and the average

now becomes 75 kg. If another man E, whose weight is 10 kg less than that of D, replaces A, then the average weight of B, C, D and E becomes 80 kg. Find A‘s weight. (1)60 kg (2) 70 kg (3) 50 kg (4) 75 kg

The average age of 8 students in a class is 20 years and the average age of the other 12 students is 15

years. Find the average age of the class. (1)17 years (2) 16 years (3) 18 years (4) 19 years

The average weekly salary per head in a firm consisting of executives and non-executives is Rs.80. The

average salary per head of the executives is Rs. 500 and that of non-executives is Rs.60. If the number of executives is 15, find the number of non-executives in the firm. (1)275 (2) 315 (3) 300 (4) 200

In what proportion must wheat at Rs.3 per kg be mixed with wheat at Rs.6 per kg, so that the mixture

be worth Rs.4 per kg.? (1)1:2 (2)1:3 (3) 3:1 (4)2:1

How much wheat at Rs.3 a kg must be added to 5 kg of wheat at Rs.6 a kg so that the mixture be worth

Rs.4 a kg.? (1)5 kg (2)10 kg (3) 8 kg (4) 9 kg

How many kilograms of sugar worth Rs 3.6/kg should be mixed with 8 kg of sugar worth Rs. 4.20/kg

such that 10% profit is made by selling the mixture at Rs. 4.4/kg? (1)4 kg (2)6 kg (3) 8 kg (4) 2 kg

24. A man purchased a goat and a sheep for Rs. 1300. He sold the sheep at a profit of 20% and the goat at a profit of 25%. His total profit was 23%. Find the cost price of the goat. (1)800 (2) 500 (3) 780 (4) 520

25. Ramesh sells 1/3 of his goods at 20% profit and the remaining at 10% loss, what would be his over -all profit or loss percentage? (1)10 (2) 0 (3) 5 (4) -10

26. In what ratio should water (available free) be mixed with milk costing Rs 12 per liter so as to make a profit of 25% by selling the diluted liquid at Rs. 13.75 per liter (1)11:1 (2)12:1 (3) 1:11 (4) 1:12

Pure milk is sold at Rs. 12 per liters. A milk vendor mixes water in the milk and sells the mixture at Rs.9 per liter. In what ratio did he mix milk and water? (1)3:1 (2)3:4 (3) 2:5 (4) None of these

A container contains 50 litres of alcohol. From this container, 10 litres of alcohol was taken out and

replaced by water. This process was repeated once more. How much alcohol is now left in the container? (1)30 litres (2)32 litres (3) 40 litres (4) 41 litres

29. From a solution which has milk and water in the ration 3: 2, 20% of the solution is removed and

replaced with water. What will be the ratio of milk and water in the resultant solution? (1)1:1 (2)12:13 (3) 1:2 (4) 13:12

Page | 76



Permutations & Combinations

Permutations: -

Basic Principle of multiplication: - If there are two tasks A & B to do. Let N1 be the number of ways to

do the task A & let N2 be the number of ways in which task B can be done then the number of ways in which both task A and B together can be done is: N1 * N2

Basic Principle of Addition: - If there are two tasks A & B to do. Let N1 be the number of ways to do the

task A & let N2 be the number of ways in which task B can be done then the number of ways in which either task A or B can be done is: N1+N2

Arrangement of N things in N way: -

To do N things in N ways we always have N! Options.

If questions consist of some conditions then those conditions are to be satisfied first before arranging others.

There can be two types of conditions either positive or negative

If question have both the conditions together then first satisfy the positive condition and then satisfy the negative condition.

If conditions collide then make the cases and add all the cases to get the final answer.

Circular Permutation: -

If N things are arranged around circular tables then we have (N-1)! Ways to arrange them.

Combinations: -

If we have to select the objects in random manner i.e. order is not important then it is called as combination.

Combination is nothing but permutation divided by N!

Pigeonhole Principle: -

If ―k + 1‖ or more pigeons are placed in k holes, then at least one hole contains 2 or more pigeons.

Page | 77



Questions 1. A person has 3 shirts & 2 sweaters. In how many ways he can wear either a shirt or a sweater (1) 6 (2) 5 (3) 2 (4) 3

2. A person has 3 shirts & 2 sweaters. In how many ways he can wear a shirt and a sweater (1) 6 (2) 5 (3) 2 (4) 3

3. In how many ways 5 prizes can be given to 5 girls so that each girl gets one prize (1) 60 (2) 120 (3) 24 (4) None of these

4. In how many ways 5 boys can stand in a row (1) 60 (2) 120 (3) 24 (4) None of these

5. In how many ways 5 boys can sit on 5 chairs in row (1) 60 (2) 120 (3) 24 (4) None of these

6. In how many ways 5 prizes can be given to 5 girls so that each girl gets one prize & first prize cannot be given to girl A or B

(1) 48 (2) 72 (3) 24 (4) 120

7. In how many ways 5 boys A, B, C, D, E can sit on 5 chairs in a row so that ―A‖ will sit on either 2nd

or 3rd

chair & B will not sit on 4th

or 5th

chair (1) 48 (2) 72 (3) 24 (4) 120

8. In how many ways 5 boys A, B, C, D, E can sit on 5 chairs in a row so that ―A‖ wants to sit on either 4th or 5

th

chair & B does not wants to sit on 2nd

or 3rd

chair (1) 48 (2) 72 (3) 24 (4) 120

9. There are 6 tasks and 6 persons. Task1 cannot be assigned to person 1 or person 2. Task2 must be assigned to person 3 or person 4 every person is to be assigned one task. In how many ways can this assignment be done? (1) 144 (2) 72 (3) 180 (4) 192

10. In how many ways 5 girls (A, B, C, D, E) can sit in five chairs if girl A doesn‘t wants to sit on 1st or 2

nd &

girl B want to sit on 2nd

or 3rd

chair? (1) 36 (2) 18 (3) 12 (4) 30

11. How many four digit numbers can be formed using digits 2, 4, 5, 8 if repetition of digit is allowed?

(1) 16 (2) 24 (3) 256 (4) 40

12. In above question what will be the answer if repetition is not allowed? (1) 16 (2) 24 (3) 256 (4) 40


How many four digit numbers can be formed using 0, 1, 2, 5, and 6

13. Repetition is allowed

(1) 120 (2) 500 (3) 625 (4) None of these

14. Repetition is not allowed (1) 120 (2) 24 (3) 96 (4) None of these

15. How many will be even if repetition is allowed (1) 120 (2) 240 (3) 480 (4) None of these

16. How many will be odd in above question? (1) 120 (2) 260 (3) 480 (4) None of these

Page | 78



17. How many will be even if repetition is not allowed? (1) 36 (2) 24 (3) 60 (4) None of these

Direction for questions 18-22: -

18. In how many ways we can arrange the word ―DONUT‖ (1) 120 (2) 24 (3) 96 (4) 60

19. In how many ways we can rearrange the word ―DONUT‖ (1) 120 (2) 24 (3) 96 (4) None of these

20. In how many ways DONUT can be arranged so that vowels are always together (1) 48 (2) 24 (3) 72 (4) None of these

21. In how many ways DONUT can be rearranged so that vowels are always together (1) 47 (2) 48 (3) 72 (4) None of these

22. In how many ways we can arrange DONUT so that vowels are not together (1) 48 (2) 24 (3) 72 (4) None of these

23. The letters of the word WOMAN are written in all possible orders and these words are written out as in a dictionary, then the rank of the word 'WOMAN' is

(1) 117 (2) 120 (3) 118 (4) 119

24. What will be the addition of all the 4 digit numbers that can be formed using digits 2, 3, 4, 5? (1) 66600 (2) 93234 (3) 92324 (4) 93324

25. Eight boys have to be seated in eight chairs numbered 1 to 8 in row. In how many ways this seating can be done such that if a particular boy does not want to sit in the first four chairs and another boy want to sit in either

7th

or 8th

chair? (1) 6! (2) 6*6! (3) 8* 6! (4) 6*7!

26. A new flag with vertical stripes is to be designed using some or all of the colours yellow, green, blue & red. The number of ways this can be done such that no two adjacent stripes have same colour is: (1) 12*81 (2) 16*192 (3) 20*125 (4) 24*216

27. How many integers greater than 999 but not greater than 4000 can be formed with the digits 0, 1, 2, 3 & 4 so that repetition is not allowed?

(1) 375 (2) 500 (3) 376 (4) None of these

28. In how many ways a committee of 3 members can be formed out of 7 persons (1) 42 (2) 21 (3) 35 (4) None of these

29. Teerth, in a hurry, stuffed 3 pairs of red socks, 2 pairs of black socks and 2 pairs of grey socks in his bag. What is the minimum number of socks he should take out to have at least one pair of left and right socks of the same colour?

(1) 7 (2)3 (3) 2 (4) 8

30. The number of candidates who appeared for a job interview from Dehradun, Chennai, Thane and Bhopal are 4, 4, 3 and 2 respectively. What minimum number of job offers would ensure that at least one candidate from Chennai is selected?

(1) 10 (2)5 (3) 7 (4) 9

Page | 79



Probability Some Important Points to remember

DEFINITION: Probability is a measure of the likeliness that an event will happen. Thus,

Probability of an event occurring =

number of favourable outcomes

total number of possible outcomes

BOUNDARIES ON PROBABILITY: If all outcomes are favourable for a certain event, its probability is 1. If none of the possible outcomes are favourable for a certain event or if a favourable outcome is impossible, then the probability is 0. In other words all probabilities are between 0 and 1. Thus 0 ≤ P ≤ 1.

COMPLEMENTARY EVENTS: Two events are complementary when one event occurs if and only if the other does not. The sum of the probabilities of complementary events is always one. The complement of an event A is denoted by A‘.

ODDS

IN FAVOUR: The ratio of the probability of an event to the probability of its complement; i.e., the ratio of favourable outcomes to unfavourable outcomes.

ODDS AGAINST: The ratio of the probability of complement of an event to the probability

of event, i.e., the ratio of unfavourable outcomes to favourable outcomes.

TO CONVERT ODDS INTO PROBABILITY:

a

When the odds in favour of an event is a : b, the probability of the event occurring is a b .

b

When the odds against an event is a : b, the probability of the event occurring is a b .

MUTUAL EXCLUSIVE & NON-EXCLUSIVE EVENTS: Two events A and B are said to be mutually exclusive when through the occurrence of one of them, the other event cannot take place or vice versa otherwise they are Non-exclusive. Note that by definition, mutually exclusive events cannot occur simultaneously. Thus, complementary events are mutually exclusive.

INDEPENDENT & DEPENDENT EVENTS: Two or more events are said to be independent if the happening or non-happening of any one does not depend on the happening or non-happening of any other. Other they are called dependent events

ADDITION LAW OF PROBABILITY: The probability that one of the several mutually exclusive events

A, B, C,.. will happen is the sum of the individual events, i.e., P = P1 + P2 + P3

... Where P1, P2, P3... are respectively the probabilities of events A, B, C and so on. This rule has to be applied if one of the events A or B have to occur.

MULTIPLICATION LAW OF PROBABILITY: If P1 is the probability that an event A happens and P2

is the probability that an event B happens, then P1 x P2 is the probability that these events happen

simultaneously or in any order if these events are independent.

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NOTE: If the events are dependent then the product P1 x P2 gives the probability that A and B occur in the order of A first and B later. In this case the happening of B depends upon the happening of A (dependent events)

and P2 is the probability that B happens after A has happened. (The value of P2 would be different if A had not happened). This law has to be applied when events A and B (both) are to happen.

SPECIFIC TYPES OF PROBLEMS: Problems in probability require some specific knowledge about

(a) coins (2) dice and (c) pack of cards

A fair (unlike the coin with our Jai in SHOLAY) coin has two different faces-one head and one tail.

A dice has six faces - each of which is marked with a number from 1 through 6. On throwing/rolling a dice, the value of the number on the face which faces upwards is said to be the value of the dice.

A pack of cards consist of 52 cards which belong to four suites (13 in each suite)-namely spades, hearts, diamonds and clubs. Each suite consists of 9 numbered cards marked from 2 through 10 and 3 picture cards a Knave (or jack), a queen and a king. The card with a letter A on it is referred to as an ace. The colour of the cards belonging to the suites of spades and clubs is black, while the rest are red.

Page | 81



Questions

Questions 1 to 5: In a single throw of a dice, find the probability of getting

an odd number.

(1) 1/ (2) 1/ (3) 1/ (4) 2/ 2 3 4 3

a number > 4.

(1) 1/ (2) 1/ (3) 1/ (4) 2/ 2 3 4 3

a prime number.

(1) 1/ (2) 1/ (3) 1/ (4) 2/ 2 3 4 3

a number <= 4.

(1) 1/ (2) 1/ (3) 1/ (4) 2/ 2 3 4 3

a multiple of 4.

(1) 1/ (2) 1/ (3) 1/ (4) 1/ 2 3 4 6

Questions 6 to 13: A number is randomly chosen from the first 50 natural numbers. Find the probability of it being a

perfect square.

(1) 4/ (2) 9/ (3)7

/

50 (4) None of these

25 50 a multiple of 5.

(1) 2/ (2) 1

/

10 (3)

1/

5 (4) None of these

5 a prime number < 29.

(1) 2

/ (2) 1

/

10 (3)

1/

5 (4) None of these

5 a perfect cube.

(1) 2/ (2) 1/ (3) 3/ (4) 3/ 25 10 50 25

a multiple of 4 or 5.

(1) 2

/ (2) 1

/ (3) 11/ (4) 3

/

5 5 25 5 a multiple of 7 or 11

(1) 2/ (2) 6/ (3) 11/ (4) 11/ 25 25 25 50

a factor of 100.

(1) 9/ (2) 4/ (3) 2/ (4) 9/ 100 25 25 50

a square root of a number < 1000.

(1) 31/ (2) 16/ (3) 31/ (4) 33/ 100 25 50 50

Page | 82



Questions 14 to 20: A coin is flipped three times. Find the probability of getting

a heads exactly once.

(1) 1/ (2) ¼

(3) 3/ (4) 1/ 8 8 2

tails exactly twice.

(1) 1/ (2) 3

/

8 (3)

1/

8 (4) None of these

4 heads all three times.

(1) 1/ (2) 1/ (3) 3/ (4) 1/ 8 4 8 2

a tails at least once.

(1) ¼

(2) 7

/ (3) 1

/ (4) 3

/

8 8 8 a heads at least two times.

(1) 3

/ (2) 1

/ (3) 1

/ (4) 1

/

8 4 8 2 a heads in the first throw, a tails in the second, and a heads in the third.

(1) 1

/ (2) 1

/ (3) 3

/ (4) 1

/

8 14 8 2 a heads in the third toss, if in the first two tosses the coin landed tails.

(1) 1/ (2) 1/ (3) 7/ (4) 1/ 2 8 8 4

Questions 21 to 24: From a pack of 52 cards, a card is chosen at random. Find the probability of it being

a king.

(1) 1/ (2) 1/ (3) 1/ (4) 1/ 13 4 2 52

a card of club.

(1) 1/ (2) 1

/

4 (3)

1/

13 (4) 1/

2 26 a 9 of diamond.

(1) 1

/ (2) 5

/ (3) 1

/ (4) 1

/

26 52 13 52 a queen of spade or club.

(1) 1/ (2) 3/ (3) 1/ (4) 1/ 13 26 26 4

Questions 25 to 29: A bag contains 5 maroon, 6 brown and 9 green balls. Find the probability that a ball drawn

at random

is either maroon or brown or green.

(1) 0 (2) 19/ (3) 21/ (4) 20/ 20 20 20

is brown.

(1) 1

/ (2) 7

/ (3) 3

/ (4) 9

/

4 10 10 20 is maroon or brown.

(1) 11/ (2) 1/ (3) 3/ (4) 7/ 20 4 4 10

Page | 83



is brown or green.

(1) 11/ (2) 1/ (3) 3/ (4) 7/ 20 4 4 10

is not brown.

(1) 1/ (2) 7/ (3) 3/ (4) 9/ 4 10 10 20

Questions 30 to 35: From a pack of cards, two cards are chosen at random. Find the probability that

one of them is a Jack and the other an Ace.

(1) 2/ (2) 1/ (3) 8/ (4) 4/ 663 221 663 663

both are Sevens.

(1) 1

/ (2) 4

/ (3) 1

/ (4) 1

/

1326 52C2 13 221 the two cards are different in some way.

(1) 0 (2) 1 (3) 1

/ (4) 4

/

221 221 one card is a 5 of diamonds and the other an 8 of spade.

(1) 1

/ (2) 1

/

663 (3)

2/


1326 both the cards belong to the same suite.

(1) 16/ (2) 3/ (3) 4

/


17 17 the cards belong different suites but of the same colour.

(1) 1/ (2) 13

/

51 (3)

13/


4

Questions 36 to 41: A pair of dice are rolled. Find the probability that the two numbers thrown up

are identical.

(1) 1 (2) 1/ (3) 1/ (4) 1/ 6 3 18

are different.

(1) 1

/ (2) 5

/ (3) 1

/ (4) 1

/

6 6 3 4 form a sum that is even.

(1) 4/ (2) 1/ (3) 5/ (4) 1/ 9 2 9 3

form a sum which is a multiple of 5.

(1) 5/ (2) 1/ (3) 2/ (4) 7/ 36 6 9 36

differ by 2.

(1) 1

/ (2) 4

/ (3) 1

/ (4) 2

/

6 9 3 9 differ by at least 1.

(1) 1

/ (2) 5

/ (3) 1

/ (4) 1

/

6 6 3 4

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Questions 42 to 46: A bag contains 4 violet balls, 6 blue balls and 1 grey ball. Two balls are drawn at random.

Find the probability that

neither of them is grey.

(1) 9/ (2) 10/ (3) 9

/


11 11 both of them are blue.

(1) 2/ (2) 3/ (3) 4/ (4) 6/ 11 11 11 11

one of them is violet and the other blue.

(1) 6/ (2) 12/ 55

(3) 18/ (4) 24/ 55 55 55

neither of them is violet.

(1) 6

/ (2) 21/ 55

(3) 49/ (4) 8

/

55 55 11 one of them is grey.

(1) 1

/ (2) 2

/ (3) 1

/ (4) 1

/

11 11 10 5 If P(E) is the probability that an event will occur, which of the following must be false?

(1) P(E)=1 (2) P(E) = 1

/ 2 (3) P(E) = 1

/ 3 (4) P(E) =-1

What is the probability of an event if the probability of its complement is 4

/5 ?

(1) 1/ (2) 2/ (3) 3/ (4) 4/ 5 5 5 5

49. If the probability of an event is 5/7 what is the probability of its complement?

(1) 2

/ (2) 3

/ (3) 4

/ (4) 5

/

7 7 7 7 Questions 50 to 52: In an exam, the probability that A solves the problem is 1/3, B solves the problem is 1/4

and C solves the problem is 1/5. Find the probability that

any two of them solves the problem

(1) 2

/ (2) 3

/ (3) 4

/ (4) 9

/

60 60 60 60

only one of them solves the problem

(1) 6/ (2) 12/ (3) 8/ (4) 32/ 60 60 60 60

the problem is solved

(1) 2/ (2) 3

/

5 (3)

4/

11 (4) 6/

11 11

Questions 53 & 54: The probability of an event is 8

/15 .

What are the odds for the event?

(1) 7:8 (2) 8:7 (3)7:15 (4) 8:15

What are the odds against the event (the odds for its complement)?

(1) 7:8 (2) 8:7 (3) 7:15 (4) 8:15

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