tcs important apti

8/4/2019 Tcs Important Apti

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PERMIT SOLUTIONSTCS PATTERN

Instructions

Before the Test:

(1) Keep only the identity card, pencil, eraser and sharpener with you. DO NOT KEEPwith you books, rulers, slide rules, drawing instruments, calculators, cellular phones, stopwatches or any other devices or loose paper.(2) Ensure that your name and roll number have been entered in the space providedcorrectly.(3) Directions for answering the questions are given before each group of questions.Read these directions carefully and answer the questions by darkening the appropriatecircles on the Answer Sheet. Each question has only one correct answer.(4) All questions carry one mark each questions.(5) Each wrong answer carries .5 negative marks for each question.(6) Do your rough work only on the test booklet and NOT on the Answer Sheets

How to Answer:(1) This test contains one section with 35 questions. You have 1 hour 30 minutes tocomplete the 105 questions.


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1. The difference between the ages of two of m y three grandchildren is 3. Myeldest grandchild is three times older than the age of my youngest grandchild andmy eldest grandchild's age is two years more than the ages of my two youngestgrandchildren added together. How old is my eldest grandchild?

(a) 12 (b) 13 (c) 10 (d) 15

Solution:Let X be the elder, Y be the younger, Z be the youngest.

From qn,1. X=3Z,2. Y-Z=3 or X-Y=33. X=2+Y+Z. Compare 2 and 3, X-Y=3 is not possible.

We need X value so get Y value and Z value from 2 and 3 respectively.Substitute in 3, we get X=15.

2. A greengrocer was selling apple at a penny each, chickoos at 2 for a penny andpeanuts at 3 for a penny. A father spent 7 pennies and got the same amount ofeach type of fruit for each of his three children. What did each child get?(a) 1 apple, 2 chickoos, 2 peanuts(b) 1 apple, 2 chickoos, 1 peanut

(c) 1 apple, 3 chickoos, 2 peanuts(d) 1 apple, 1 chickoos, 1 peanut

Solution:Get the answer from options.No of items * no of children*cost of item=total cost for the item.A)1apple*3 =3*1 =3,2chickoos*3 =6*(1/2) =3,2peanuts*3 =6*(1/3) =2. The sum of cost is 8. . It doesnt matches with father cost. Sothis is wrong answer.

B)1apple*3 =3*1 =3,2chickoos*3 =6*(1/2) =3,1peanuts*3 =3*(1/3) =1. The sum of cost is 7. It matches with father cost. So this iscorrect answer.

3. The IT giant Tirnop has recently crossed a head count of150000 and earnings of$7 billion. As one of the forerunners in the technology front, Tirnop continues tolead the way in products and services in India. At Tirnop, all programmers areequal in every respect. They receive identical salaries and also write code at thesame rate. Suppose 12 such programmers take 12 minutes to write 12 lines of

code in total. How long will it take 72 programmers to write 72 lines of code intotal?

(a) 12 (b) 18 (c) 6 (d) 72

Solution:12 programmers take 12 mins to write 12 lines of code.(Programmers = (1/ time) = lines of code ).72 programmers take 12 mins to write 72 lines of code.

4. Alok and Bhanu play the following min -max game. Given the expression


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N = 9 + X + Y Z ,where X, Y and Z are variables representing single digits (0 to 9),Alok would like to maximize N while Bhanu would like to minimize it. Towards thisend, Alok chooses a single digit number and Bhanu substitutes this for a variableof her choice (X, Y or Z).Alok then chooses the next value and Bhanu, the variableto substitute the value. Finally Alok proposes the value for the remaining variable.Assuming both play to their optimal strategies, the value of N at the end of thegame would be

(a) 20 (b) 18 (c) 27 (d) 0

Solution:

The most appropriate answer for the equation X+Y-Z is 11

5. One day Rapunzel meets Dwarf and Byte in the Forest of forgetfulness. Sheknows that Dwarf lies on Mondays, Tuesdays and Wednesdays, and tells the truthon the other days of the week. Byte, on the other hand, lies on Thursdays, Fridaysand Saturdays, but tells the truth on the other days of the week . Now they makethe following statements to Rapunzel - Dwarf: Yesterday was one of those dayswhen I lie. Byte: Yesterday was one of those days when I lie too. What day is it?

(a) Monday (b) Sunday (c) Thursday (d) Saturday

Solution:Monday Tuesday Wed Thursday Friday Saturday Sunday

Dwarf T T TByte T T T

Condition: Both of them says yesterday is one of the day I lied.They didnt mention anything on Sunday. So left that.Monday is not possible Bcoz they didnt mention anything on Sunday.Tue and wed is not possible Bcoz Dwarf speak true on Mon and Tue.

In Thursday, Dwarf speaks lie. So the statement he said is false.In the case of Byte, he speaks true on Thursday. So the statement he said is also trueand satisfies the condition. So answer is Thursday.

6. The citizens of planet nigiet are 8 fingered and have thus developed theirdecimal system in base 8. A certain street in nigiet contains 1000 (in base 8)buildings numbered 1 to 1000. How many 3s are used in numbering thesebuildings?

(a) 192 (b) 64 (c) 54 (d) 102

Solution:Here base is 8.

No of 8 in 10 (1,2,3,....10) is1*base (8)0

No of 8 in 100 (1,2,3,...100) is2*base(8)1

No of 8 in 1000(1,2,3,...1000) is 3*base(8)2 and so on...

The value of3*(8)2 is192.


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7. On planet zorba, a solar blast has melted the ice caps on its equator.8 yearsafter the ice melts, tiny planetoids called echina start growing on the rocks. echinagrows in the form of a circle and the relationship between the diameter of thiscircle and the age of echina is given by the formulad = 4 * (t - 8) for t 8 where d represents the diameter in mm and t the number ofyears since the solar blast. Jagan recorded the radius of some echina at aparticular spot as 8mm. How many years back did the solar blast occur?

(a) 8 (b) 12 (c) 16 (d) 24

Solution:Given: d=8mm.

To find years:

d = 4 * (t - 8), substitute d value.t=12.

8. A circular dartboard of radius 1 foot is at a distance of20 feet from you. Youthrow a dart at it and it hits the dartboard at some point Q in the circle . What is theprobability that Q is closer to the centre of the circle than the periphery?

(a) 1/4 (b) 1/2 (c)3/4 (d) 1/3

Solution:Condition: probability for dart is closer to the centre of the circle than the

periphery.Let the circle be 1m radius. If the dart is lies i nside the m radius i.e. the dart is closerto centre is less than the periphery. So

Area of circle (radius m) = /4

Area of circle (radius 1 m ) = P = (chances to lies inside the 1/2 circle)/(Chances to lies inside the full circle)

P = (/4) / ( )= 0.25

9) A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, thetotal number of wheels in the schoolyard was 166. What could the possiblenumber of bicycles?

(a) 14 (b) 10 (c) 12 (d) 11

Solution:Total no wheels =166. To find total no of bicycles.Get the answer from solution.A) 14*2=28wheels (166-28) =138B) 10*2=20 wheels (166-20) =146C) 12*2=24 wheels (166-24) =142D) 11*2=22 wheels (166-22) =144. From the above which one is divided by 4 is thecorrect answer. I.e. 144/4=32 four wheeler and 11 bicycles.

10) 9years ago, Andromedas age was twice Achilles age .9 years hence,Andromedas age will be 4/3 times the age of Achilles. Find Andromedas presentage in binary numbers.


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(a)11011 (b) 11000 (c) 1001 (d) 1010

Solution:Let Andromeda as A, Achilles as B.

A-9 =2(B-9) A-2B=-9;A+9= (4/3) (B+9) 3A-4B=9;Solve the above 2 eqn, we get A=27.Convert A value into binary, answer as 11011.

11. After the typist writes 12 letters and addresses 12 envelopes, she inserts theletters randomly into the envelopes (1letter per envelope). What is the probabilitythat exactly 1 letter is inserted in an improper envelope?

(a) 11/12 (b) 0 (c) 1/12 (d) 1/6

Solution:Let if she put one letter in wrong envelope, another one letter is to be

placed in wrong envelope only. So the probability of exactly one letter inserted inimproper envelope is 0.

12. Alok is attending a workshop "How to do more with less" and today's theme isworking with fewer digits. The speakers discuss how a lot of miraculousmathematics can be achieved if mankind (as well as womankind) had only workedwith fewer digits. The problem posed at the end of the workshop is How many 5digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) thatare divisible by 4?Can you help Alok find the answer?

(a) 375 (b) 625 (c) 500 (d) 3125

Solution:

Condition for divisibility by 4 is last 2 digits must be divisible by 4.Among the five numbers (1, 2, 3, 4, 5) have to find the combination which are divisible by4.The combinations are 12, 24,32,44,52.First three digit is 5*5*5 and remain two digit is 5 so answer is 5*5*5*5

13. Given 3 lines in the plane such that the points of intersection form a trianglewith sides of length 20, 20 and 30, the number of points equidistant from all the 3lines is

(a) 1 (b) 0 (c) 4 (d) 2

Solution:The point having equal distance in both side is equidistant.From given only one point having the same length. So answer is 1.

14) 21 people meet and shake hands. The maximum number of handshakespossible if there is to be no cycle of handshakes is (A cycle of handshakes is asequence of people a1, a2, ,aKsuch that the pairs (a1, a2), (a2, a3), , (a (k -1), a k) , (ak, a1) shake hands.

(a) 17 (b) 18 (c) 19 (d) 20


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Solution:If cyclic handshake, no of handshakes= no of people.If non cyclic handshake, no of handshakes= no of people -1.

15) The ticket to Disneyland will cost anywher e from 1p to 63p. You need toproduce the exact change as the ticket counter and have with you a 63p coin. Soyou decide to break this into change but you want to carry with you as few coinsas possible. Assuming that coins of all denominations are availab le, how many

coins (denominations) would you split the 63p into?

(a) 33 (b) 63 (c) 6 (d) 64

Solution:This problem split the coins in denomination of 2n. n be the no of coins.n=5, 20 + 21 +22 +23 +24 +25 =63

16. For the FIFA world cup, Paul the octopus has been predicting the winner ofeach match with amazing success. It is rumoured that in a match between 2 teamsA and B, Paul picks A with the same probability as A's chances of winning. Let'sassume such rumours to be true and that in a match between Ghana and Bolivia,Ghana the stronger team has a probability of2/3 of winning the game. What is theprobability that Paul will correctly pick the winner of the Ghana - Bolivia game?

(a) 5/9 (b) 1/9 (c) 2/3 (d) 1/3

Solution:

Condition:If Paul picks A with some probability as As chance of winning.

If they having chance of losing is 1/3, Pauls predictions to be same.From the Qn,Ghana team is 2/3 strong.Probability of predicting the winning team = {(2/3)*(2/3)} + {(1/3)*(1/3)}

= 5/9

17. 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In otherwords, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3 }, ...,{a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest haveshaken hands with at least one person in the set is

(a) 18 (b) 13 (c) 34 (d) None

Solution:Condition:

Hands must be shaking in circular fashion.Have to form a small group; they must shake their hands at least with one person

in the rest.

Take the middle person from three members.Out of 36, you can able to form a small set of people is 12.


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18. One the Planet, Oz, there are 8 days in a week Sunday to Saturday andanother day called Oz day. There are 36 hours in a day and each hour has 90 minwhile each minute has 60 sec. As on earth, hour hand covers the dial twice everyday. Find the approximate angle between the hands of clock on Oz when time is12.40 am

(a) 89 (b) 251 (c) 111 (d) 79

Solution:

Angle covered by hour hand in 1 hour = 360/18 = 20 degree.In one min 20/90=2/9 degreeAngle covered by minute hand in one min=360/90=4 degRelative deg difference=4-2/9=34/9Now -240+34/9*40=88.88 degree.

19. The IT giant Tirnop has recently crossed a head count of150000 and earning of$7 billion. As one of the forerunners in the technology front, Tirnop continues tolead the way in products and services in India. At Tirnop, all programmers areequal in every respect. They receive identical salaries ans also write code at thesame rate Suppose 12 such programmers take 12 minutes to write 12 lines of codein total. How many lines of code can be written by 72 programmers in 72 minutes?

(a) 6 (b) 432 (c) 72 (d) 12

Solution:12 lines of code are written in 12 * 12 = 144 programmer minutes1 line of code is written in 144/12 = 12 program mer minutesWe now have 72 * 72 programmer minutes Lines of code that can beWritten = 72 * 72 /12 = 432

20. A hollow cube of size 5 cm is taken with a thickness of1 cm. It is made ofsmaller cubes of size 1 cm. If 4 faces of the outer surface of the cu be are painedtotally how many faces of the smaller cubes remain unpainted?

(a) 900 (b) 488 (c) 500 (d) 800

Solution:Formula for hollow cube=n3(n-2)3

Each 1*1 cube has 6 facesTotal 1*1 cubes =53- (5-2) 3 = 98Total faces of small cubes = 98*6 = 588Now, four sides of the 5*5 cube is paintedSo, total small cube faces painted = 4*5*5 = 100

answer = 588-100 = 488

21. Planet fourfi resides in 4 dimensional space and thus the currency used byits residents are 3 dimensional objects. The rupees notes are cubical in shapewhile their coins are spherical. However the coin minting machinery lays out somestipulations on the size of the coins.

The diameter of the coins should be at least 64mm and not exceed 512mmGiven a coin, the diameter of the next larger coin is at least 50% greater. The diameter of the coin must always be an integer.


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You are asked to design a set of coins of different diameters with theserequirements and your goal is to design as many coins as possible . How manycoins can you design?

(a) 5 (b) 8 (c) 9 (d) 6

Solution:

Given next one should be 50 % more

Start with1st coin 642)64+32=96........3)96+48=144.4)144+72= 216........5)216+108=324........6)324+162=486.....7)486+243 is greater than 512 so we stopped here. Ans is 6

22. A hare and tortoise a race along a circle of100 yards diameter. The tortoisegoes in one direction and the hare in the other. The hare starts after tortoise hascovered 1/5 its distance and that leisurely. The hare and tortoise meet when thehare has covered only 1/8 of the distance. By what factor should the hare increaseits speed so as to tie the race?

(a)8 (b) 37.80 (c) 40 (d) 5

Solution:

After tortoise covers 1/5th distance hare starts the race.

When hare covers 1/8th of distance tortoise meets hare

So distance covered by tortoise = 1-(1/5 + 1/8)= 27/40Time taken by both is same ,time = dist/speedSo (dist/ speed) of tortoise = (dist / speed) of hareLet speed of tortoise be t and of hare be h27/40t = 1/8hh = (40/(8*27) )* t = 5/27 * t

Now for the next part hare has to cover 7/8 th distance when tortoise covers 1/8 thdistanceso we get1/8t = 7/8h h = 7tso the factor by which h's speed increases = 7t/ (5/27 * t)

which we get as 37.8

23. Anoop managed to draw 7 circles of equal radii with their centres on thediagonal of a square such that the two extreme circles touch two sides of thesquare and each middle circle touches two circles on either side . Find the ratio ofthe radius of the circles to the side of the square.

(a) 1:(2 + 7 2) (b) 1:(4 + 7 3) (c) (2 + 72):1 (d) 1:(2 + 62)

Solution:The extreme circles will have radius perpendicular to sides...so the part of diagonal tillthe centre of circle will be sqrt (2) r.


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[Make diagram and it will be clear].now remaining portion is r , 5 more circles will contribute 10r and last circle will contributesqrt(2)r + r.

Total: 12r + 2sqrt (2) r = sqrt (2) side

so ratio of radius to side = 1 :( 2+6sqrt (2))

24. Ferrari S.p.A. is an Italian sports car manufacturer based in Maranello, Italy.Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsoreddrivers and manufactured race cars before movin g into production of streetlegalvehicles in1947 as Ferrari S.p.A. Throughout its history the company has beennoted for its continued participation in racing especially in Formula One where ithas enjoyed great success. Rohit once bought a Ferrari. It cou ld go 2 times as fastas Mohits old Mercedes. If the speed of Mohits Mercedes is 32 km/hr and thedistance travelled by the Ferrari is 952 km, find the total time taken in hours forRohit to drive that distance.

(a) 15.88 (b) 29.75 (c) 14.88 (d)476

Solution:Rohit : Ferrari , Mohit : MercedesLet speed of car be x km/h Let speed of car be y km/hAccording to the question, x=2yWe know that y=32 km/h.x=2X32 ==>64 km/h.Total time taken in hours for Rohit to drive that distance:Distance travelled/speed = 952/64=14.875 hours.

25. There are two boxes, one containing 10 red balls and the other containing 10green balls. You are allowed to move the balls between the boxes so that whenyou choose a box at random and a ball at random from the chosen box, theprobability of getting a red is maximized. This maximum probability is

37/38 (b) 1/2 (c) 14/19 (d) 3 / 4

Solution:Take one red ball in 1st bag.Put the remaining nine red ball with 10 green ball in other bagProbability of red ball in 1st bag=1/2Probability of red in other bag= (1/2)*(9/19)

The required probability=p(A)+p(B)

=1/2+9/38 =28/38=14/19.

26 .Pizza shops make pizzas of same thickness but different diameter. Cost ofpizza A with diameter8 cm is 80 $, cost of the pizza B with diameter12 cm is 240$, cost of the pizza B with diameter24 cm is 720 $. Which of the above mentionedpizzas gives the best value for money?

(a) A (b) B (c) C (d) Cannot be determined


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Solution:A 8 cm = 80$ - 1 cm=10$B 12 cm = 240$ -1 cm =20$C 24 cm= 720$ -1 cm=30$So cheapest is A .

27. Determine the distance between x-intercept and z-intercept of the plane whoseequation is 6x+8y-3z=72.

(a) 31.92 (b)26.83 (c) 32.66 (d) 25.63

Solution:Sqrt of ((d/a)^2+(d/c)^2) d=72 a=6 b=8 c=-3

(d/a)^2=144(d/c)^2=576

Sqrt(144+576)=26.83

28. Lucy finds around 25 groups of stars that appear to her as constellations. Shedraws 7 patterns of the constellations in her notebook and notes down the numberof stars in each of them. She counts 5 stars in first constellation and 15 on next.She counts a number the third time and forgets to note it down. The next fourconstellations she counts 51.53,159,161. Next day her father looks at the notebookand wants to know the number of stars in the third constellation. Lucy onlyremembers that number of starts counted in each of the constellation followed apattern 5,15, x, 51, 53, 159, 161.

(a) 19 (b) 17 (c) 47 (d) 31

Solution:5 x 51 159 ; 15 53 159

15*3+6=5151*3+6=159;5*3+2=1717*3+2=5353*3+2=161;

29. 6 persons standing in the queue for ROBERT movie, are wearing differentcolour shirts. All of them belong to different age group, after two years theiraverage age will be 43 and seventh person joined with them, hence the currentaverage age has become 45. Find the age of seventh person?

(a) 67 (b) 69 (c) 72 (d) 74

Solution:After 2 yrs, avg age is 43;Before 2 yrs, avg age is 41;

Sum of ages of 6 mem=41*6=246;7th mem is added, the avg =45;Sum of ages of 7 mem=45*7=315;7th mem age =315-246=69;


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30. X is 6 years younger to Y. X's father is a businessman who invested 10000/ - at8% rate of interest and obtained his amount after 10 years. Y's father is a jobholder who invested around 20000 at 2% rate and obtained his amount after 20years. Now Compounded both of them get around Rs. ABC .After5 years the ratioof ages of X and Y is 1:2. Now X's father is 20 years older to Y and Y' father is 30years more than X. After20 years again X's mother asks X's father to purchase aLCD TV which costs around 45000/-. What is the age of X and Y together?

(a) 12 (b) 8 (c) 18 (d) 6

Solution:X+6=Y(X+5)/(Y+5) = (1:2)

X-Y=-62X+10=Y-5 2X-Y=-5. Solve above 2 eqn we get ans as x+y=1+7=8

31. The great musician Rahman has orga nized a live concert. The concert isorganized in a big auditorium. Rahman plays both English and Tamil songs on his

Yamaha Casio. The audience in the Eastern part of the auditorium love listening toTamil Songs and those in the western part of the auditorium . He plays songs inrandom. The probability that he plays English songs for 6 consecutive times is 1in

(a) 32 (b) 16 (c) 64 (d) 128

Solution:Possible events is English and Tamil=2

Favourable is English =1.So prob for playing one eng song is 1/2.For consecutive 6 times is 1/ (26) =1/64.

32. It is dark in my bedroom and I want to get two socks of the same color from mydrawer, which contains 24 red and 24 blue socks. How many socks do I have totake from the drawer to get at least two socks of the same colour?

(a) 3 (b) 25 (c) 48 (d) 26

33. A person was fined for exceeding the speed limit by 10mph. Another personwas also fined for exceeding the same speed limit by twice the same. If the secondperson was traveling at a speed of 35 mph, find the speed limit.

(a) 35mph (b) 15 mph (c) 20 mph (d) 30 mph

Solution:

I st person exceeds the limit is 10mph.2nd person exceeds twice the limit i.e. 20mph2nd persons speed is 35 mph.So the speed limit is (35-20) =15mph.


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34. A person drives with constant speed and after some time he sees a milestonewith 2 digits. Then travels for1 hour and sees the same 2 digits in reverse order.1hour later he sees that the milestone has the same 2 digits with a 0 between them.What is the speed of the car?

(a) 54 (b) 45 (c) 27 (d) 36

Solution:

Let x = the 1st digit on the first mile stoneLet y = the 2nd digitLet s = speed of the car"Then travels for 1 hour and sees the same 2 digits in reverse order."10x + y + 1s = 10y + x10x - x + s = 10y - y9x + s = 9y 1"1 hours later he sees that the milestone has the same 2 digits with a 0 between them."10y + x + s = 100x + y10y - y + s = 100x - x9y + s = 99x 2Rearrange the above two equations for elimination9x - 9y + s = 0-99x+9y + s = 0 ----------------adding eliminates y-90x + 2s = 02s = 90x s = 45xx has to equal 1, then s = 45 mph (If x=2 and s=90 mph, when added toa two digit milestone, could not be at another two digit milestone.)Find y9x + s = 9y9(1) + 45 = 9y9 + 45 = 9y simplify divide by 9

y=6Speed is 45 mph

Answer:1st milestone: 16travel one hr +452nd milestone: 61travel one hr: +453rd milestone: 106

35. With four fifths of then tank full, a vehicle travels 12 miles. How much distancewill the vehicle travel with one third tank full?

a)8.05 km (b) 6.05 km (c) 12km (d) 5 km

Solution:

4/5 of full tank travels=12 miles.Full tank travels =15 miles.One-third full tank=15/3=5 miles.1 miles =1.609km. So 5miles =5*1.609=8.05km.

36) Peter is twice as old as Paul was when Peter was as old as Paul is now . Thecombined age of Peter and Paul is 42 years. How old is peter now?


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(a) 21 (b) 18 (c) 24 (d) 26

37) There are two water tanks A and B, A is much smaller than B. While water fillsat the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160., intank B. (At the end of first hour, B has 10 litres, second hour it has 20, and so on)If tank B is 1/16 filled after17 hours, what is the total durations required to fill itcompletely?

(a) 4 hours (b) 21hours (c) 22 hours (d) 24 hours

Solution:Every hour amount of water in tank B gets doubled than previous hour.

If the time increases by an hour, then the amount of water in th e tank gets doubled.Initially 1/16 of tank in 17hrs.2*(1/16)=1/8 of tank in 18 hrs.2*(1/8) = 1/4 of tank in 19 hrs2*(1/4) =1/2 of tank in 20 hrs2*(1/2) =1 i.e. of full tank in 21 hrs.

38) Middle-earth is a fictional land inhabited by hobbits, Elves, dwarves and men .The Hobbits and the Elves are peaceful creatures who prefer slow, silent lives andappreciate nature and art. The dwarves and the men engage in physical games.The game is as follows. A tournoi is one, where out of two teams that play amatch, the one that loses get eliminated. The matches are played in differentrounds where in every round; half of the teams get eliminated from thetournament. If there are 10rounds played in a knock -out tournoi how manymatches were played?

(a)1024 (b) 1023 (c)1026 (d)1011

Solution:No of players = 2^n.No of matches=(2^n)-1

39) Ferrari S. p. A. is an Italian sports car manufacturer based in Maranello. Italy.Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsoreddrivers and manufactured race cars before moving into production of street -legalvehicles in 1947 as Ferrari S.p.A. Throughout its history, the company has beennoted for its continued participations in racing, especially in Formula One, whereit has enjoyed great success Rohit once bought a Ferraris. It could go 4 times asfast Mohits old Mercedes. If the speed of Mohits Mercedes is 35 km/hr and thedistance travelledby the Ferrari is 968km, find the total time taken for Ro hit to

drive that distance.

(a) 242 hours (b) 27 hours (c) 7 hours (d) 6.91 hours

Solution:

Rohit: Ferrari, Mohit: MercedesLet speed of Ferrari car be x km/h Let speed of car Mercedes be y km/hAccording to the question, x=4yWe know that y=35 km/h.x=4X35 ==>140km/h.Total time taken in hours for Rohit to drive that distance:


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Distance travelled/speed = 968/140=6.914hours.

40) Two blocks of copper with density of 100 kg/m^3 are twisted into wires oflength 100 km and thickness 0.1mm. Copper is a very ductile material. Its ductilityis measured in terms of percentage elongation upon application of tensile forces.The conductivity of the copper wire is extremely high rendering it useful in theconstruction of many electronic circuits. If the voltage through one such circuit is18 V and the current flowing in the circuit is 190 ma. What is the resistance of thewire?

(a) 208.00 K Ohms (b) 3420.00 K Ohms (c) 0.09 k Ohms (d) 10.56 KOhms

Solution:Ohms law, V=IR.V= 18,I=190mA.

R=0.09kohms.

41) 5 men and 5 women meet and men dance with women. Which of the followingare always true? A. there are 2 men who have danced with same number ofwomen. B. There are 2 women who have danced with same number of men.

(a) Both A and B (b) A only(c) B only (d) Neither A nor B

Solution:

Its just logical.

42) Three boys John, Tom and Oliver and two girls Rachel and Kim are to beseated in a row. Rachel always sits to the left of John. No girl sits at the extremepositions and at the middle positions. Tom always sits at the extreme positions.Who sits to the right of Kim?

(a) Oliver (b) Tom (c) Tomor Oliver (d) John

Solution:Given, girls wont sit in extreme and middle. So 2girls in 2 and 4 position only .Rachel sits left of john. So john is in middle. Right of Kim is extreme position. So tom orOliver is answer.

43) The thank giving banquet at No.2, Ritcher Street, had 49 guests whichconsisted of 6 statesmen, 26 relatives and their families. At the end of a banquet

19 people shake hands with other , some of which were between the statesmenalone, some between relatives alone and some between the statesmen a ndrelatives. How many handshakes will there be in total?

(a) 342 (b) 171 (c) 180 (d) 162

Solution:nCr.

n=19, r=2 ==171.

44) There are 7 children. You are told that the youngest child is a boy. Theprobability that all of them are boys is 1 in


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(a) 64 (b) 21 (c) 2 (d) 128

Solution:Possible events is boy and girl=2Favourable is boy =1.So prob for getting one boy is 1/2.For consecutive 6 times is 1/ (26) =64.

45) Given a collection of points P in the plane, a 1-set is a point in P that can beseparated from the rest by a line, . i.e. the point lies on one side of the line whilethe others lie on the other side. The number of1 -sets of P is denoted by n1(P). Theminimum value of n1(P) over all configurations P of 5 points in the plane ingeneral position (.i.e. no three points in P lie on a line) is

(a) 3 (b) 5 (c) 2 (d)7

Solution:Consider plane is like triangle. Separating one point and rest by a line.Minimum lines required will be 3 .

46) Given a collection of points P in the plane, a 1 -set is a point in P that can beseparated from the rest by a line, . i.e. the point lies on one side of the line whilethe others lie on the other side. The number of1 -sets of P is denoted by n1(P). Themaximum value of n1(P) over all configurations P of 5 points in the plane ingeneral position (.i.e. no three points in P lie on a line) is

(a) 3 (b) 5 (c) 2 (d)7

Solution:Maximum value will be 5 it will occur when all points are aligned in a circle

47) There is a pie to be divided among 20 people. A man eats3 pizza, a women eatstwo pieces and a child eats half a piece of pie . Find the number of men, womenand children so that they are 20 people in total and everyone gets some pie. Thereare 20 pieces of pie in all.

(a) 7 women, 1 men and 12 children(b) 5 women, 1 men and 14 children (c) 6women, 2 men and 12 children(d) 4women, 2 men and 14 children

Solution:Backtracking from the answer.

a)7w*2=141m*3=312*1/2 =6, total=23people.

b)5w*2=101m*3=314*1/2=7, total=20 people.

48)A number when divided by D leaves a remainder of8 and when divided by 3Dleaves a remainder of21 . What is the remainder left, when twice the number isdivided by 3D?


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(a) 13 (b) 42 (c) 3 (d) cannot be determined

Solution:Number=Divisor * Quotient + Remainder.N=D*Q+8N=3D*Q1+21D=13/ (Q-3Q1)Q-3Q1! =0.

Take Q=4, Q1=1,D=13.Substitute in above eqn, get N=60.2N/3D=? Remainder is 3.

49)In a pizza restaurant, you get a basic pizza with two toppings, ch eese andtomato. You can also make up your own pizza with extra toppings. You can alsochoose from 10 different toppings, e.g. olives, ham, mushroom, salami etc. Rosswants to order a pizza with 2 different extra toppings. How many differentcombinations are possible?

(a) 100 (b) 1024 (c) 90 (d) 45

Solution:Its a combination problem. nCr,n=10,r=2.Answer is 45

50) The Thousand Pillar Temple of Hyderabad was built by the Kakatiyans ofChalukyan dynasty in the 12th century. Each pillar has carvings made of blockmonolithic rocks of basalt which are polished to give it a brilliant look. One sunnymorning, three tourists visit the temple. Samantha is taller than Lily and taller thantwo of the thousand pillars and Kelly is shorter than Samantha and the pillars.Which of the following statements would be more accurate?

(a) Its impossible to tell (b) Kelly is as tall as Lily(c) Lily is shorter than Kelly (d) Lily is taller than Kelly

Solution:Given statements are not sufficient to answer. So answer is a.

51) Franchois Pachet, a researcher at Sony Computer Science Laboratories isalso a jazz musician. He decided to build a robot able to improvise like a pro.Named Continuator, the robot duet can with alive musician in real- time. It listensto a musical phrase and then computes a complementary phrase with the sameplaying style. If the cost of making the robot is divided between materials, labour

and overheads is the ratio of 4:5:2. If the materials cost $ 84.0, the cost of therobot is

(a) 184.80 $ (b) 189.00 $ (c) 231.00 $ (d) 462.00 $

Solution:Given:Material cost is 84$. In ratio material is 4x. So x=21.Total sum of ratio is 11x.Total cost =11*21=231$


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52) The great Indian mathematician Bhaskaracharya formulated this problem inthe twelfth century for his teenaged prime number aged daughter Lilavati. He alsoauthored the eponymous Lilavati, a compendium of mathematical puzzles, inwhich the number of problems that use this formula is the sum of two primenumbers. The product of the two prime numbers is smaller than the total numberof problems in the Lilavati. Now, if the difference of any two numbers is 4 and theirproduct is 18, what is the sum of their squares?

(a) 34 (b) 40 (c) 52 (d) 42

Solution:Formula :(a-b)2=(a2+b2-2ab)

Given a-b=4 ab=18, substitute in above eqn , get answer as 52

53) A taxi driver commenced his journey from a point, and drove 10 km towardsnorth, and turned to his left and drove another 20 km. After waiting to meet afriend here he turned to his right and continued to drive another50 km. In whichdirection is he now?

(a) North (b) South (c) West (d) East

Solution:

Starting towards north.Ending also in north only.

54) A result of global warming is that the ice of some glaciers is melting . Twelveyears after the ice disappears tiny plants, called lichens, start to grow on therocks. Each lichens grows approximately in the shape of a circle. The relationshipbetween the diameter of this circle and the age of the lichen can be approximatedwith the formula d = 13 * (t-11) for t > 11 where d represents the diameter of thelichen in millimetres, and t represents the number of years after the icedisappeared. Using the above formula, calculate the diameter of the lichen, 36years after the ice has disappeared.

(a) 468 mm (b) 457 mm (c) 325 mm (d) 11 mm

Solution:

Given t=36 years, we need to find d using the formula in question.

55) The British mathematician Lewis Caroll also loved to make up fantastic storiesin which he embedded a number of clever puzzles and curious riddles. Forexample, his popular story, Alice in Wonderland, is about young girl called Alicewho dreams of a strange world where she meets several unusual charactersincluding the Red Queen and the March hare. In our story, after2 years of time,Paul will be twice as old as Alice. Presently he is 6 times as old. How old is Paulnow?

(a) 2 (b) 4 (c) 3 (d) 6


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Solution:Let present age of Paul be P and Alice be A.From qn :

A=P/6;P- 2A=2;

Sub A value, we get P=3.

56) A long, thin strip of width 10cm is kept on a flat surface. Another identical stripis kept on it as an overlapping manner such that the combined width of the two is

15cm.What is the width if22 such strips kept like this?

(a) 115 cm (b) 110 cm (c) 200 cm (d) 95 cm

Solution:Let X be the initial width of strip, Y be the width of the newly added strips, Z is the no ofstrips.

(Z-1)*(Y-X)+X.From qn. X=10, Y=15, Z=22.

57) A toy train produces at least 10 different tunes when it moves around a circulartoy track of radius 5 meters, at 10 meters per minute. However, the toy train isdefective and it now produces only two different tunes at random. What are theodds that the toy train produces3music tunes of the same type (1 in _____ ) ?

(a) 3 (b) 9 (c) 8 (d) 458) Fill dirt or fill soil is usually the sub-soil removed from an excavation side andis used to level a place or create artificial mounds. If the average density of sub soil removed from a site is 3gm/cu cm and it weight 400 kg. How manyhemispherical pits each of volume 240 cubi c cm, can this sub-soil fill?

(a) 555 (b) 277 (c) 556 (d) 554

Solution:Its very simple.No of hemispheres =amt of soil in cu.cm/ vol of hemisphere in cu.cm.Amount of soil=400kg=400000gm.Amount of soil in cu.cm=400000/3=133333.33 cu.cmVolume of 1 hemispherical pits=240 cu.cm.No of hemispheres=133333.33/240=555 pits.

59) The New York Public library is on of the worlds greatest repositories of booksand journals. It has a beaut iful reading room facing Manhattans famous FifthAvenue. In the reading rooms are 10 reading spots. Each reading spot consists of

a round table with 4 chairs placed around it. There are some readers such that ineach occupied reading spot there are different numbers of readers. If in all thereare 10 readers, how many reading spots are empty?

(a)None (b)6 (c)5 (d)4

Solution:1st spot=1reader2nd spot=2 reader3rd spot=3 reader4th spot=4 reader.10 readers can occupy 4 spots only. So answer is 6


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60) A group of friends Tom, Tim, Dick, Diana, Harry, and Harriet go out to a fairthree hundred meters from the Mc.Donalds which is five KMs away. They see aweighing machine and decide to have some fun. However the girls refuse to stepon the weighting machine. So Tom,Dick and harry, weigh themselves in aparticular order. First Tom, Dick, and Harry weigh themselves individually andthen tom and Dick, Dick and Harry, Tom and Harry and then Tom, Dick and harrytogether respectively. The recorded weight for the last measure is 158 kgs. Theaverage of all the 7 measures is

(a) 112.86 (b)52.67 (c)90.29 (d)67.71

Solution:1st Tom2nd dick3rd harry4th tom + dick5th dick + harry6th tom + harry7th tom + dick + harry.Average of 7 measures=4(T+D+H)/7=4*158/7=90.29

61) In the year 2002, Britain was reported to have had 4.3m closed -circuittelevisions (CCTV) camerasone for every 14 people in the country . This scrutinyis supposed to deter and detect crime. In one criminal case, the policeinterrogates two suspects. The ratio between the ages of the suspects is 6:5 andthe sum of their ages is 66 years. After how many years will the ratio be 8:7?

(a) 11 years (b) 12 years (c) 6 years (d) 7 years

Solution:A/6 =B/5=x;A=6x;B=5x;A+B=66; == x=6;A=36, B=30;After X years ,((A+X)/(B+X))=(8/7)Solve the above eqn, we get X=12.

62. A sheet of paper has statements numbered from 1 to 40. For each value of nfrom 1 to 40, statement n says "At least n of the statements on this sheet are true ."Which statements are true and which are false?

a) All statements are falseb) The odd numbered statements are true the even numbered are falsec) All statements are trued) The even numbered statements are true and the odd numbered are false

Solution: its just logical.

63.10 suspects are rounded by the police and questioned about a bank robbery.Only one of them is guilty. The suspects are made to stand in a line and eachperson declares that the person next to him on his right is guilty. The rightmostperson is not questioned. Which of the following possibilities are true?


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(A) All suspects are lying or the leftmost suspect is innocent. (B) All suspects are lying and the leftmost suspect is innocent.

(a) A only(b) B only(c) Both A and B(d) Neither A nor B

64. The pace length P is the distance between the rear of two consecutivefootprints. For men, the formula, n/P = 144 gives an approximate relationshipbetween n and P where, n = number of steps per minute and P = pace length inmeters. Bernard knows his pace length is 164cm. The formula applies to Bernardswalking. Calculate Bernards walking speed kmph.

(a) 236.16 (b) 11.39 (c) 8.78 (d) 23.62

Solution:P be the pace length in metres, N be the no steps per minute.N/1.64 = 144N = (144 * 1.64) = 236.16

No. of steps per minute = 236.16Distance per minute = N*P= (236.16 * 164) cmDistance per minute = 0.3873024 kmDistance per hour = 23.238144

Speed = 23.238144 km/h

65. Alice and Bob play the following coins-on-a-stack game.20 coins are stackedone above the other. One of them is a special (gold) coin and the rest are ordinarycoins. The goal is to bring the gold coin to the top by repeatedly moving thetopmost coin to another position in the stack. Alice starts and the players taketurns. A turn consists of moving the coin on the top to a position i below the topcoin (0 i 20). We will call this an i-move (thus a 0-move implies doing nothing).The proviso is that an i-move cannot be repeated; for example once a playermakes a 2-move, on subsequent turns neither player can make a 2 -move. If thegold coin happens to be on top when it's a player's turn then the player wins thegame. Initially, the gold coin is the third coin from the top. Then

(a) In order to win, Alices first move should be a 0-move.(b) In order to win, Alices first move should be a 1 -move.(c) Alice has no winning strategy .

(d) In order to win, Alices first move can be a 0 -move or a 1-move

Solution: I dont know explanation. All the staff saying this one is correct.

66) Paul the octopus who has been forecasting the outcome of FIFA world cupmatches with tremendous accuracy has now been invited to predict ICC world cupmatches in2011. We will assume that the world cup contenders have been dividedinto 2 groups of 9 teams each. Each team in a group plays the other teams in thegroup. The top two teams from each group enter the semi finals (after which thewinner is decided by knockout). However, Paul has a soft spot for India and when


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India plays any team, Paul always backs India. Alas, his predictions on matchesinvolving India are right only 2 out of 3 times. In order to qualify for the semi finals,it is sufficient for India to win 7 of its group matches. What is the probability thatIndia will win the ICC world cup?

(a) (2/3)^10 (b) (2/3)^9 + 8/3 * (2/3)^9

(c) 8/3 * (2/3)^9 (d) (2/3)^10 + 8/3*(2/3)^9

Solution:(2/3)^10 + 8/3*(2/3)^9

67) A sheet of paper has statements numbered from 1 to 40. For each value of nfrom 1 to 40, statement n says "At least n of the statements on this sheet are true ."Which statements are true and which are false?

a) The first 26 statements are false and the rest are true. b) The odd numbered statements are true the even numbered are falsec) The first 13 statements are true and the rest are false. d) The even numbered statements are true and the odd numbered are false

Solution:none of the above.

68) There are two water tanks A and B, A is much smaller than B. While water

fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80,

160, in tank B (At the end of first hour, B has 10 liters, second hour it has 20,

and so on). If tank B is 1/32 filled after 11 hours, what is the total durations

required to fill it completely?

(a)5 Hours (b) 15 Hours (c) 17 Hours (d)16 Hours

Solution:Every hour amount of water in tank B gets doubled than previous hour.

If the time increases by an hour, then the amount of water in the tank ge ts doubled.Initialiy 1/16 of tank in 11hrs.2*(1/16)=1/8 of tank in 12 hrs.2*(1/8) = 1/4 of tank in 13 hrs2*(1/4) =1/2 of tank in 14 hrs2*(1/2) =1 i.e. of full tank in 15 hrs.

69) A sheet of paper has statements numbered from 1 to 10. For all values of n

from 1 to 10, statement n says At most n of the statement on this sheet is false.

Which statements are true and which is false?

(a)All the statements are FALSE

(b) The odd numbered statements are true and the even numbered are false.(c) The first half statements are true and the rest are false.

(d) The even numbered statements are true and the odd numbered are false.

70) A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday,

the total number of wheels in the schoolyard was 90. What could be possible

number of bicycles?

(a)12 (b) 14 (c) 10 (d)11

Solution:


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Total no wheels =90. To find total no of bicycles.Get the answer from solution.A) 12*2=24wheels (90-24) =66B) 14*2=28 wheels (90-28) =62C) 10*2=20 wheels (90-20) =70D) 11*2=22 wheels (90-22) =68. From the above which one is divided by 4 is the correctanswer. I.e. 68/4=17 four wheeler and 11 bicycles.

71.Six friends decide to share a big cake. Since all of them like the cake, theybegin quarreling as to who gets to first cut and has a piece of the cake . One friendsuggests that they blindfold a friend and then choose from a well shuffled set ofcards numbered from one to six. You check and find that this method works as itshould be simulating a fair throw of a die. Y ou check by performing multiplesimultaneous trials of picking the cards blindfolding and throwing a die. You notethat the number shown by the method of picking up a card and throwing a realworld die, sums up to a number between 2 and 12. Which total would be likely toappear more often8, 9 or10?

(a) 8 (b) 9 (c) 10 (d) All are equally likely.

Solution:Combination of 8 is 2+6,3+5,4+4,5+3,6+2.Combination of 9 is 3+6,4+5,5+4,6+3.Combination of 10 is 4+6,5+5,6+4.

72. Consider two tumblers, the first containing one litre of coffee. Suppose youtake one spoon of water out of the first tumbler and pour it into the secondtumbler and after which you take one spoon of the mixture from the secondtumbler and pour it back into the first tumbler. Which one of the followingstatements holds true?

(a) There is less coffee in the first tumbler than water in the secondtumbler.

(b) There is more coffee in the first tumbler than water in the second tumbler(c) There is as much coffee in the first tumbler as there is water in the

second tumbler(d) None of the statements holds true.

Solution:Think logically.

73.A lady has fine gloves and hats of different colours in her closet - 18 blue, 32red and 25 yellow. The lights are out and it is tot ally dark. In spite of thedarkness, she can make out the difference between a hat and a glove. She takes

an item out of the closet only if she is sure that it is a glove. How many glovesmust she take out to make sure that she has a pair of each colour?

(a) 6 (b) 8 (c) 60 (d) 59

Solution:This problem we cant take exactly what we need. So go for worst case i.e. if we takeMaximum of different colours. From the given red color is highest. So take the count .Then take the next highest is yellow. Totally we get 32+25= 57, in that surely we canget exactly 2 pair of socks of different color among three color. To get one more pair,take one pair . so totally she have to take 32+25+2=59.


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74.It was the semester exam day, Vidhya caught the college bus . She enjoyedtravelling by bus. Moving at 6 mph, the bus took Vidhya to college at the righttime. She finished her exam and had a chit chat with her friends and suddenlyshe realized that it was 6 pm and she had missed the college bus. She decidedto walk back home at 4 mph. What is her average speed for the day?

(a) 4 mph (b) ) 5 mph (c) 2.4 mph (d) 4.8 mph

Solution:Its just to find average speed = (2*6*4)/(6+4)

= 4.8mph

75. Spores of a fungus, called late blight, grow and spread infection rapidly.These pathogens were responsible for the Irish potato famine of the mid -19century. These seem to have attacked the tomato crops in England this year.The tomato crops have reduced and the price of the crop has risen up . Theprice has already gone up to $45 a box from $27 a box a month ago. How muchmore would a vegetable vendor need to pay to buy 27 boxes this month overwhat he would have paid last month?

(a) $27 (b) $ 18 (c) $45 (d) $ 486

Solution:Vendor paid extra = amount paid this month amount paid last month.

=27*45 -27*27=486

76.A car manufacturer produces only red and blue models which come out ofthe final testing area completely at random. What are the odds that 5consecutive cars of the same color will come through the test area at a time?

(a) 1 in 16 (b) 1 in 125 (c) 1 in 32 (d) 1 in 25

77.Given a collection of 36 points in the plane P and a point X equidistant

from all points in P, which of the following are necessarily true?A. The points in P lie on a circle.B. The distance between any pair of points in P is larger than the distance

between X and a point in P(a) A only (b) B only (c) Both A and B (d) Neither A nor B

78.Susan made a block with small cubes of 8 cubic cm volume. To make theblock she used 3 small cubes long, 9 small cubes wide and 5 small cubes deep.She realizes that she has used more small cubes than she really needed. Sherealized that she could have glued a fewer number of cubes together to lock likea block with same dimensions, if it were made hollow . What is the minimumnumber of cubes that she needs to make the block?

(a) 114 (b) 135 (c) 21 (d) 71

Solution:Formula for making hollow cube= (3*9*5) - ((3-2) (9-2) (5-2))

=135-21=114.

79.A seamstress buys a certain amount of Gingham cloth which comes in rollsthat are exactly 56 inches wide. She has also bought a certain length of Seeksucker cloth and 35 inches wide. The seamstress first focuses on the Gingham


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roll ad discovers that she has 116 yards of Gingham and she wants to dividethe gingham into 116 lengths of1 yard each. She wants to have tw ice as manypieces of seek sucker as she does of the Gingham. It takes 4 seconds to cuteach length of Gingham. Working non-stop, how long (in seconds) will it takeher to cut all 116 pieces?

(a) 464 (b) 460 (c) 463 (d) 465

Solution:To make 116 pieces, we have to cut 115 times, for each cut it takes 4 secs.For 115 cuts =115*4=460

80.A man goes north 37km,turns left goes 2km,turns right goes 17 km againturns right goes another2km. Find distance between the starting & the endingpoint.

(a) 56 (b) 52 (c) 58 (d)54

Solution:

2

172 37+17=54

37

N

81.A research lab in Chennai requires 100 mice and 75 sterilized cages for a

certain set of laboratory experiments.

To identify the mice, the lab has preparedlabels with numbers 1 to 100, by combining tags numbered 0 to 9. The SPCArequires that the tags be made of toxin-free material and that the temperature ofthe cages be maintained at 27 degree Celsius. Also, not more than 2 mice canbe caged together and each cage must be at least 2 sq.ft in area. The 5experiments to be conducted by lab are to be thoroughly documented andperformed only after a round of approval by authorities. The approvalprocedure takes around 48 hours. How many times is, the tag numbered '4'used by the lab in numbering these mice?

(a) 9 (b) 19 (c) 20 (d) 21

Solution:No of 4 in 10 (1,2,3,....10) is 1*base (10)0

No of 4 in 100 (1,2,3,....100) is2*base (10)1

82. A triangle is made from a rope. The sides of the triangle are 25 cm, 11 cmand 31 cm. What will be the area of the square made from the same rope?

(a) 280.561 (b) 280.563 (c) 280.564 (d) 280.562


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Solution:Area of the Square= ((perimeter of triangle)/4) 2

i.e. perimeter of triangle is sum of the sides.

83. Mr. Alex is the father of children Jane, Joe, and Jill. He goes to a nearbypark twice a week. He loves his children very much. On a certain day, on hisway to the park he finds fruit vendors selling different fruits. Watermelon is onepenny each, dates at 2 for a penny and plums at 3 for a penny . Mr.Alex spent 7

pennies and got the same amount of each type of fruit for each of his threechildren. What did each child get?(a)1 Watermelon, 2 Dates, 1 plum (b) 1 Watermelon, 1 Date, 1 plum

(c) 1 Watermelon, 3 Dates, 2 plums (d) 1 Watermelon, 2 Dates, 2 plums

Solution:Get the answer from options.No of items * no of children*cost of item=total cost for the item.A)1watermelon*3 =3*1 =3,2dates*3 =6*(1/2) =3,1plum*3 =3*(1/3) =1. The sum of cost is 7. . Its matches with Mr.Alexs cost. So this iscorrect answer.

84.An athlete decides to run the same distance in 1/4th less time that sheusually took. By how much percent will she have to increase her averagespeed?

(a) 25% (b) 50% (c) 33.33% (d) 20%

Solution:Speed is inversely proportional to time.Let he takes time t at speed s.

now new time is 3/4t , so speed will become 4/3sso speed is 1.33s , that is speed increases by 33.3%

85. Alok and Bhanu play the following coins in a circle game. 99 coins arearranged in a circle with each coin touching two other coins . Two of the coinsare special and the rest are ordinary. Alok starts and the players take turnsremoving an ordinary coin of their choice from the circle and bringing the othercoins closer until they again form a (smaller) circle. The goal is to bring thespecial coins adjacent to each other and the first player to do so wins the game.Initially the special coins are separated by tw o ordinary coins O1 and O2. Whichof the following is true?

(a) In order to win, Alok should remove O1 on his first turn.(b) In order to win, Alok should remove one of the coins different from O1

and O2 on his first turn(c) In order to win, Alok should remove O2 on his first turn.(d) Alok has no winning strategy.

Solution:There are two special coins separated by two ordinary coin. If Alok removesone out of these two ordinary coin say O1 or O2, Bhanu will remove the otherordinary coin and join both the special coins and win the game . Hence choice(a) is ruled out.Total 99 coins. Reducing the two ordinary coin and the two special coins, the


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remaining ordinary coins other than O1 and O2 and special coins S1 and S2, is 95ordinary coins surrounded by special coins. If Alok starts removing one out ofthese 95ordinary coins and Bhanu will remove the second ordinary coin and thiswill continue and Alok will remove the 95 th ordinary coin and join the two specialcoin from out side and win the game.

86. A racehorse starts chasing a wild pony 3 hours after the pony bolts thestable. The pony runs through the entire country of Alb. Texas jumping 3

streams and crossing four 10 meter roads. The racehorse finally catches upwith the pony after four hours by the time the sun had set and the moon was upin the sky for 4 hours. If the average speed of the racehorse is 73kmph thenaverage speed of the wild pony is?

(a) 54.75 kmph (b) 42.71 kmph (c) 31.29 kmph (d) 41.71 kmph

Solution:Time taken to catch the pony by horse is 4 hrs. So distance is 73*4.

The average speed of pony is distance/time=(73*4) / (4+3)= 41.71 kmph

87.On planet Korba, a solar blast has melted the ice caps on its equator. 9 years

after the ice melts, tiny planetoids called echina start growing on the rocks .Echina grows in the form of circle, and the relationship between the diameter ofthis circle and the age of echina is given by the formula d= 4*v (t-9) for t = 9 ,where d represents the diameter in mm and t, the number of years since thesolar blast. Anubhav recorded the radius of some echina at a particular spot as7mm. How many years back did the solar blast occur?

(a) 17 (b)21.25 (c) 12.25 (d) 12.06

Solution:Given: d=7mm.

To find years:

d = 4 * (t - 9), substitute d value.t=21.25.

88.How many 13 digit numbers are possible by using the digits 1, 2, 3, 4, 5which are divisible by 4 if repetition of digits is allowed?

(a) 4*5 (b) 512 (c) 5*12! (d) 5

Solution:

Condition for divisibility by 4 is last 2 digits must be divisible by 4.

Among the five numbers (1, 2, 3, 4, 5) have to find the combination which are divisible by4.The combinations are 12, 24,32,44,52.First eleven digits are 511 and remain two digit is 5 so answer is 5 11*5

89.In a family there are some boys and girls. All boys told that they are havingequal number of brothers and sisters and girls told that they are having twicethe number of brothers than sisters. How many boys and girls are present in afamily?


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(a) 5 boys & 3 girls (b) 7 boys & 2 girls (c) 4 boys & 3 girls (d) 6 boys & 2girls

Solution:Its just logical. Go from answer.c) Satisfying the given condition.

90.Mr Behera wants to build a house for his wife . In his dream house there are 5rooms each having equal area. The length of each room is 4 m, breadth is 5 mand the height is 2m. For every single unit of area, he requires 17 bricks, howmany bricks are required to make the floor of a particular room?

(a) 340 (b) 420 (c) 280 (d) 400

Solution:They asked for floor alone. So we need to find the area for floor. Take length andbreadth ,calculate area?L=4m, B=5m, A=20m2.Per unit 17 bricks needed , for 20 = 20*17=340

91. The Mehtas have decided to launch their perfumes and have narroweddown to five ingredients for the perfume: Lilac, Balsamic, Lemon, Woody andMimosaic. The customer can order for specific variety of perfume. To make aperfume that is in demand the Mehtas adhered to the following conditions:Lilac and Balsamic go together. Woody and Mimosaic go together; Woody andBalsamic never go together. Lemon can be added with any material. All of thefollowing combinations are possible to make a perfume except___.

(a) Balsamic and Lilac (c) Mimosaic and Woody(b) Woody and Lemon (d) Mimosaic and Lilac

Solution:Conditions:Perfume combinations: Li+ B, W+M , W+B wont ,L can be added to all.From the given option d) option wont sa tisfy the given conditions.

92.Ifa and b are mixed in 3:5 ratio and b, c are mixed in 8:5 ratio and if thefinal mixture is 35 litres. Find the amount of b in the mixture.

(a) 15.73 (b) 14.73 (c) 15.24 (d) 14.24

Solution:a/c=a/b *b/c=24/25.

a:b:c=24:40:25Totally (24 + 40 + 25)x=35;The amount of B in the mixture is =40*(x=35/89)=15.73

93. The Chennai corporation has a particular strategy for assigning numbers forbuildings. The Corporation had strict rules that every building should have anumber. In T Nagar, a place in Chennai there many buildings were underresidential category. For buildings, the Corporation numbered from 1 to 100.For shops, corporation numbered between 150 and 200 only in prime numbers.How many times does the number6 appear in the building numbers?


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(a) 20 (b) 19 (c) 10 (d) 13

Solution:No of 6 in 10 (1,2,3,....10) is 1*base (10)0

No of 6 in 100 (1,2,3,...100) is 2*base(10)1

No of 6 in 1000(1,2,3,...1000) is 3*base(10)2 and so on...

The value of1*(10) is10.

94.A Person buys a horse for 15 pounds, after one year he sells it for 20pounds. After one year, again he buys the same horse at 30 pounds and sells itfor 40 pounds. What is the profit for that person?

(a) 20 pounds (b) 15 pounds (c) 25 pounds (d) 10 pounds

Solution:Simple calculation.First time he gets 5 pounds.Next time he gets 10 pounds. Totally he got 15 pounds as profit.

95.A scientist was researching on animal behaviour in his lab. He was veryinterested in analyzing the behaviour of bear. For some reason he travelled 1mile in the north direction & reached the North Pole. There he saw a bear andthen followed the bear around 1 hr with a speed of 2km/hr in east direction.After that he travelled in south direction & reached at his lab in 2 hrs. Then whatcolour is the bear?

(a) White (b) black (c) brown (d) grey

Solution:Its just logical. Going north = white; south =black.

96. Three boys Bob, Pete and Oliver and two girls Samantha and Kristie are to

be seated in a row. Samantha always sits to the left of Bob. No girl sits at the

extreme positions and at the middle positions. Peter always sits at the extreme

positions. Who sits to the right of Kristie?

(a)Peter or Oliver (b) Bob (c) Peter (d)Oliver

Solution:Given, girls wont sit in extreme and middle. So 2girls in 2 and 4 position only.Samantha sits left of Bob. So Bob is in middle. Right of Kristie is extreme position. SoPeter or Oliver is answer.

97.If x/2y =2a, then 2x/x-2ay=?(a) 4 (b) ay (c) 2 (d) 2a

Solution:From given x=4ay. Sub x value in (2x/x-2ay) =4

98.A man looks at a painting and tells Neither have I any brother nor any sister,but the person in the painting is my fathers son. Then who is in the painting?

(a) Father (b) Daughter (c) Son (d) Himself

Solution:


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Its just logical. Himself is answer.

99.Inspired by Fibonacci series, Sanket decided to create his own series whichis 1,2,3,7,7,22,15,67,..... What number comes immediately before 63?

(a) 31 (b) 61 (c) 57 (d) 202

Solution:Split as 1, 3, 7, 15, --, 63

2, 7, 22, 67.Take the first one the difference between no is formed as multiples of 2.2, 4, 8, 16, 32.

100) Determine the distance between the x-intercept and the z-intercept of the

plane whose equation is 2x+9y-3z=18

(a) 6.32 (b)10.82 (c)3.00 (d)5.00

Solution:Sqrt of ((d/a)^2+(d/c)^2) d=18 a=2 b=9 c=-3

(d/a)^2=81(d/c)^2=36

Sqrt(81+36)=10.82

101.A game is played between 2 players and one player is declared as winner.All the winners from first round, played in the second round. All the winnersfrom second round played in third round and so on. If8 rounds were played todeclare only one player as winner, how many players played in first round?

(a) 256 (b) 128 (c) 255 (d) 127

Solution:

No of players= 2^8

102.1/3 rd of a number is more 3 than the 1/6 of the same number, then findthe number?

(a) 24 (b) 12 (c) 18 (d) 20

Solution:Let X is the number.(1/3) X-(1/6) X=3,Solving these we can get the answer.

103.It is the class with the seating arrangement in 4 rows and 8 columns. Whenthe teacher says 'start' the girl who is sitting in first row and first column willsay 1, then the next girl sitting behind her will say 4, the next girl sitting behindthat girl will say 7, in a particular order each girl is telling a number, thefollowing girls told 10, 13 next turn is yours what you will say?

(a) 14 (b) 16 (c) 20 (d) 17

104.If Valentines day of2005 was celebrated on a Monday. What day is Feb 14,2010 ?


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(a) Monday (b) Sunday (c) Tuesday (d) Wednesday

Solution:In leap year 2 odd days

Ordinary year 1 odd days.From 2005 to 2010, there is one leap year and 4 ordinary year. So totally 6 odd days.So answer is Sunday.

105.If a pipe can fill the tank in 6 hrs but unfortunately there was a leak in thetank due to which it took 30 more minutes .Now if the tank was full how muchtime will it take to get emptied through the leak?

(a) 39 hrs (b) 78 hrs (c) 72 hrs (d) 70 hrs

Solution:Work done by the leak in 1 hour = [(1/6)-(2/13)]

= 1/78 hrs.

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