sct sample paper

8/10/2019 Sct Sample Paper

1/13

TCS ON 25 AND 26 SEPTEMBER AT NIET NOIDA==============================================================

APTITUDE PROBLEMS PROVIDED BY ONE OF MY FRIEND

Q.12 A Tree of height 36m at the edge of a road broke at a certain height.It fell in such away that its top touched other edge of the road.If the breadth of the road is 12cm thenwhat is the height at which the tree broke?

Q.14 A can complete a piece of work in 8 hours, B can complete in 10 hours and Ccan complete in 12 hours. If A,B and C work together but A leaves after 2 hours.Findthe time taken by B and C to complete the remaining work.

Q. 16 There is a water-cask with three different water-taps.

With the smallest tap, the water-cask can be filled in 30 minutes.With the middle tap, the water-cask can be filled in 20 minutes.With the largest tap, the water-cask can be emptied in 15 minutes.

The water- ask is one-fourth filled. Now each of the 3 taps is opened turn by turn for aminute each in the sequence, smallest, largest, middle, smallest, largest, middle,smallest, largest, middle.

In how much time would the water-cask be first filled?

Q. 17 Find the sum of the number of combinations possible by using 1,2,3,4 such thatno number is repeated (ex:- 1223,4322 are invalid 1234,4321 are valid)more than once.

Q.19 A man walked a certain distance south and then the same distance plus 7km duewest.He is now 13km from his starting point.What are the distances south and west thathe walked?".

Q.20 Find the sum and number of divisors of 544 excluding 1 and 544.

a.569b.589c.577d.529


2/13

Q1. A dishonest seller uses a weight of 800 gram in place of 1 kg and adds20% impurities in sugar. What would be his profit percentage it he claims tobe selling at the cost price?

50%

As 800 gm. sugar contains 20% impurities,Quantity of pure sugar in 800 gm =800*(100/120)=2000/3

If seller buys 1Kg. pure sugar at Rs.'y'=Cost Price, thenCost price of (2000/3) gm=(2000/3)*y/1000= 2y/3

%of SP 'y' compared to (2y/3) =y*100/(2y/3) = 300/2= 150So profit %= 50

Shortcut method:-If the shopkeeper sells his good at x% loss on cost ( here is profit since

impurity is mixed) price but uses Y gm instead of Z gram. Then his profit orloss % is

[100-x] z/y 100So here[100+20] 1000/800 100 = 50%

Q2. 5+7+4=3647309+6+3=456990

8+2+9=912672then

7+3+5=??????5+7+4 = 36 47 30

36 => (5*4)+5+7+4 -- (a*c)+a+b+c47 => (5*7)+5+7 --- (a*b)+a+b

30 => 5*(5+1) -- a*(a+1)

9+6+3 = 45 69 9045 => (9*3)+9+6+369 => (9*6)+9+6

90 => 9*(9+1)

Similarly

7+3+5 = x y zx => (7*5)+7+3+5 => x=50

y => (7*3)+7+3 => y=31z => 7*(7+1) => z=56


3/13

Ans : 503156

Q3. 16, 14, 24, 66, 256 , 1270, ?(16-2)*1=14(14-2)*2=24

(24-2)*3=66(66-2)*4=256

(256-2)*5=1270(1270-2)*6=7608

Q5. find the maximum value of n such that 77! is per fectly divisible by720^n

720 -> 2^4 * 3^2 * 5^1

To find the max. power of 720, it is enough to find the maximum power of"5"... Since 5 is the largest prime factor here...

77/5^1 + 77/5^2 + 77/5^3 = 15+2+0 = 17 [Quotient only]Max. power of 5 is 17... Hence max. power of 720 is "17"...

Ans : 17

Q6. Cencus population of a district in 1981 was 4.54 lacs, while in year 2001it was 7.44 lacs. What was the estimated mid-year population of that districtin year 2009.

8.6 LAKH !!P(estimate)=P1+n/N {P2-P1) WHERE n=NO. MONThs from P1 census to

date of estiMateN=NO. of months between census,P1= FIRST census,P2=secondcensus..ANSWER IS 8.6 LAKH...

Q7. Find the minimum value of n such that 50! is perfectly divisible by2520^n.

50!/2520^n

2520 -> 2^3 * 3^2 * 5^1 * 7^1

Here 7 is the largest prime factor...So in order to find the minimum value of "n", it is enough to find the


4/13

minimum power of "7"... nd for maximum value of "n", find max power of

7...

For max. value of n, find50/7^1 + 50/7^2 = 7 + 1 = 8 [quotient only]

Max. value of n which is perfectly divisible by 2520^n is (8)Min. value is 1

Max value : 8Min Value : 1

Q10. Consider there is an elevator and you are at the upside and coming

down using elevator. You walk 20 steps and then you stop, then you reachto the ground in 10 minutes. If you walk 10 steps and then stop, then you

reach to the ground in 20 minutes. What is the speed of the elevator andHow many steps are there??

Let e be the speed of the elevator, n be the no. of stepsn = 20 + 10*e = 10+20*e

e=1n=30

No. of steps : 30

Speed : 1 step/min

20 people going to one temple. (some time waste data) They want Rs. 20.

For men-Rs.3, women-Rs.2, children-50 paisa. How much money spends formen, children and women?

Let number of men be x, women y and children z

x+y+z = 20 ---(1)

men gives 3 rupees each --->total money spend by men = 3x

women gives 2 rupees each--->total money spend by women =2y

children gives 50 paisa each ---> total money spend by children = 0.5zTotal 20 rupees is given by all

3x+2y+0.5z = 20 ---(2)

Solving (1) and (2)x=1 , y=5 , z = 14


5/13

total money spend by men = 3x = Rs3

total money spend by women =2y = 2*5 = Rs10total money spend by children = 0.5z = 0.5*14 = Rs7

Q2. A bag with 100 kgs potatoes have 99% water. It is kept in the openunder the sunlight. After sometime, little amount of water got evaporated

and reduced to 98%. What is the weight now ?

100 * 99/100 = 99kg

so 99kg of water nd 1kg of potato

Given after evaporation, it gets reduced to 98%

So water only ll get evaporatedWeight of potato remains same (ie) 1kg

Let d new weight be "x"

x * 98 /100 = x-1 [ here am calculating weight of water. so subtractedweight of potato from total weight (ie) x-1]

x=50kg

so new weight = 50 Kg

Q7. If the milk and water ware added in the ratio 5:4 then how much more

water should be added so he gets the ratio of 6:7. let quantity of water should added be x then

A/Q5/(4+x)= 6/7

=> 35=24+6x=> x=11/6

ans: 11/6

Q8. Suppose there is a number 235 such that sum of first two digits is equalto the third digit. How many such 3 digits numbers are possible?

The last digit can not be 0.

If the last digit is 1, the only possible number is 101.


6/13

(Note that 011 is not a 3-digit number)

If the last digit is 2, the possible numbers are 202 and

112.

If the last digit is 3, the possible numbers are 303, 213and 123.

If the last digit is 4, the possible numbers are 404, 314,224 and 134.

If the last digit is 5, the possible numbers are 505, 415,

325, 235 and 145.

Note the pattern here - If the last digit is 1, there is

only one number. If the last digit is 2, there are two

numbers. If the last digit is 3, there are three numbers.If the last digit is 4, there are four numbers. If the last

digit is 5, there are five numbers. And so on.....

Thus, total numbers are1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

So Ans is 45 only

Q9. There is a triangle and 3 ants on each vertex of the triangle. The 3 ants

start to move randomly along the edges of the triangle. What is theprobability that two ants will collideEvery ant can move in one of two directions.

so possible 8 combinations.Only two cases are possible when two ants will not collide when all three move in same

direction.

So probability that two ants will collide = 6/8=3/4Is this solution Helpfull? Yes (3) | No (2) ARPIT SAXENA (3 MONTHS AGO)

ans = 5/6

1 case when two ants are not collide when all move in 1 direction

total cases =6 combinationleft combination =1-1/6=5/6

Q10. A person has 7 pennys with him and 1 water melon is for 1p,2chickoos for 1p, 3 grapes for 1p. He has three sons. How can he share thefruits equally?

Ans:- 1 water melon, 2 chikoos and 1 grapes to every child.


7/13

reason-->

because he has 7 penny so if he buy:

3 water melon -----> 3p6 chickoos -----> 3p

3 grapes -----> 1ptotal-> 7p

he distribute to his children:1 water melon 2 chickoos and 1 grapes to every children.

Q11. There is a water-cask with three different water-taps.

With the smallest tap, the water-cask can be filled in 30 minutes.

With the middle tap, the water-cask can be filled in 20 minutes.With the largest tap, the water-cask can be emptied in 15 minutes.

The water- ask is one-fourth filled. Now each of the 3 taps is opened turn byturn for a minute each in the sequence, smallest, largest, middle, smallest,

largest, middle, smallest, largest, middle.

In how much time would the water-cask be first filled?

Simply lets suppose tank is of 60 liter.

1/4th = 15 liter is already filled so remaining 45 liter has to be filled.

cycle is of 2 Liter - 4 Liter + 3 Liter.So average 1 liter filled in 3 min.After 43*3 min = 129 min it will be 15+43 = 58 liter

and then next 1 min the 2 liter will fill the tank.So total time 129+1 = 130

Q17. A sum of money becomes 5 1/2 times in 30 years at simpleinterest.Find the rate of interest?

(a)10%

(b)15%(c)12%(d)18%

15%

Amount A = P + PNR/100 , where P-->principal ,R-->rate and T-->time


8/13

Amount becomes 5 1/2 times principal

A = 11/2*P

11/2*P = P + PNR/10011/2 = 1 + 30*R/100

3*R/10 = 9/2

R = 15%

Or we can use direct formula ie

R= 100*(n-1)/ t

Q18. if BUCKET written as 116, then COLOUR will be written as

Question is wrong

The question is BASKET is coded as 116 then, COLOUR will be coded as____BASKET => 2+1+19+11+5+20=58 => 2*58 =116similarly COLOUR => 3+15+12+15+21+18 = 84

=> 2*84 = 168so COLOUR will be coded as 168

Q21. Find the sum of the number of combinations possible by using 1,2,3,4such that no number is repeated (ex:- 1223,4322 are invalid 1234,4321 are

valid)more than once.

total no. formed = 4!=4*3*2*1=24each digit will be used at each positions, 6 timessum of digits at unit place = 6*1+6*2+6*3+6*4 = 6*(1+2+3+4)= 60this sum will be same for hundred, tens & unit places

sum of all 4 digit numbers formed using digits 1,2,3,4= 1000*60+100*60+10*60+60

=60*(1000+100+10+1)=60*1111

=66660

Q2. WHAT IS THE ANSWER?

3 6 122 4 8

5 5 ?OPTION:

A) 5


9/13

B) 4

C) 6D) 2

(3+2)/(3-2)=5(6+4)/(6-4)=5

(12+8)/(12-8)=5hence ans=A

ts will be 15*(15-1)= 15*14= 21

Ans is 2*15C2=210.

15 th player can play with remaining 14 members two times = 2*14=28

14 th " remaining 13= 2*13=26

2*(1+2+3+4+......+14)=2(14)(14+1)/2=210

c) 210

number of games played by each player with others = 2*14=28

total number of games = (15*28)/2 = 210a game played by two players thats why we divide with 2.

Q8. Find the 8th term in sries?

2,2,12,12,30,30,.........

answer is 56.

given series is 2, 2, 12, 12, 30, 30,........

we know about the natural numbers 1, 2, 3, 4,.....

so, the series works in following way.

1 * 2 = 22 * 1 = 23 * 4 = 12

4 * 3 = 12

5 * 6 = 306 * 5 = 307 * 8 = 56

8 * 7 = 56

so its simple and our required ans is 56.


10/13

Q27. If 73+46=42,

95+87=57, than62+80=?

73+46

7-3 = 44+6 = 10(4+10)*3 = 42

95+87

9-5 = 48+7 = 15

(4+15)*3 = 57Q1. A letter is chosen at random from the word 'ASSASSINATION'. What is

the probability thatit is a vowel?

A.4/13

B.8/13C.7/13

D.6./13there are 6 vowels out of 13 letters

propability chosing vowel is 6/13

62+80

6-2 = 48+0 = 8

(4+8)*3 = 36Q15. 7528 : 5362 :: 4673 : ?

Optiona) 2367

b) 2451

c) 2531d) 2489

your question is wrong. Actual question is 7528:5306::4673:?. & answer is2451.

As there is a difference of 2222. 7528-2222 = 5306. so 4673-2222 = 2451 Q17. There are two pipes A and B.If A filled 10 liters in hour B can fills 20

liters in same time.likewise B can fill 10,20,40,80,160.... if B filled in(1/16)th of a tank in 3 hours.how much time will it take to fill completely?

1/16 in 3 hours1/8 in 4 hours,as here rate of water filling is doubled


11/13

1/4 in 5 hours

1/2 in 6 hours1 in 7 hours

ans will be 7 hours

Q20. 3,5,11,29,83,245,?

Ans is:7315-3=2

11-5=6 |2*329-11=18 |6*3

83-29=54 |18*3245-83=162 |54*3

731-245=486 |162*3

21. find the last 3 digit of 443^443.

ans:307

power is 443=>443/4 rem=3

so,443^3=86938307last 3 digit=307

Q1. A Jar contains 18 balls. 3 blue balls are removed from the jar and notreplaced.Now the probability of getting a blue ball is 1/5 then how many

blue balls jar contains initially?8th march Infosys

x/15 = 1/5x =33+3(removed 3 blue balls) = 6

Q2. A person starts writing all 4 digit numbers .How many times had hewritten the digit 3?

case 1:no of 4 digit nos with one 3 digit=4C1*9*9*9=2916case 2:no of 4 digit nos with two 3 digit=4C2*9*9=486case3:no of 4 digit nos with three 3 digit=4C3*9=36

case 4:no of 4 digit nos with one 4 digit=1

No of times we typed digit 3=(2916*1)+(486*2)+(36*3)+(1*1)=3997(ans)

Q4. 1961^21*21^19611961^21

21/4 reminder 1 ,, 1961^121^1961


12/13

1961/4 reminder 1,, 21^1

so 1961*21 = 41181

Q5. there are 16 people, they divide in to four groups,now from those four

groups select a team of three members,such that no two members in the

team shoud belong to same group

4c1*4c1*4c1*4c3=256 (4c3 means we can select any 3 teams from fourteams and each one from each team)

Also we can selelct any group in 4 ways and each can be formed in 4 * 4 *4

So 4*4*4*4=256

Q6. If a refrigerator contains 12 cans such that 7 blue cans and 5 red cans.

In how many ways can we remove 8 cans so that atleast 1 blue can and 1red can remains in the refrigerator.

possible draw 8 balls and in refrigirator contains atleast 1 blue and 1 red ballare (6,2) (5,3) (4,4)6 2---->7c6*5c2--->7*10=70

5 3---->7c5*5c3--->21*10=2104 4---->7c4*5c4--->35*5=175

70+210+175=455

ANS=455

Q30. Q. There are 6561 balls out of them 1 is heavy.find the minimum no oftimes the balls have to be weighted for finding out heavy ball

for this type question ans is cube root of ballsso ans=cube root(6561)=8

so ans is 8

explanation : make 3 groups of equal balls weight 2 groupsif any group heavy so heavy ball in heavy groups

if both weight equal then ball in third group and repeat procedure.........

Is this solution Helpfull? Yes (19) | No (10) SHYAM SUNDER GUPTA (5 MONTHS AGO)

For problems like this, just find the 3rd root of the number. For ex: consider 3 balls, u can find

the heavier by just weighing 2 balls, so min = 1. consider 9 balls, divide them into 3 equal

groups, now u can weigh 2 groups to find the group in which the heavier ball lies, and u ll be leftwith 3 and u know how to find out of 3. so its 3 pow 2 = 9, then 3 pow 3 = 27...... 3 pow 8 =

6561. So the ans is 8.


13/13

6561 if u notice is 3^8...n can be divided by 3(prime factor) only...we keep

on dividing it into sets of 3 and in 1 weighing itself you can determine whichset is heavy. Divide that set into further 3 lots...keep doing that..

65612187 2187 2187 1st weighing

729 729 729243 243 243

81 81 8127 27 279 9 93 3 3

1 1 1

ANswer is 8 attempts

Q25. Q. Find the sum of all 4 digit numbers formed using digits 1,2,5,6.Asked today in online test.(n-1)! * (111...n) *(sum of the digits)

=(4-1)!*1111*(1+2+5+6)

=93324

total no. formed = 4!=4*3*2*1=24

starting with 1 = 3*2= 6 no.s

starting with 2 = 3*2= 6 n0.sstarting with 5 = 3*2= 6 no.s

starting with 6 = 3*2= 6 no.s

sum of digits starting with 1,2,5,6 = 6*1+6*2+6*5+6*6=6*(1+2+5+6)=84

this sum will be same for hundred, tens & unit places

sum of all 4 digit numbers formed using digits 1,2,5,6

= 1000*84+100*84+10*84+84=84*(1000+100+10+1)

=84*1111

=93324

Q27. Q. Find the 8th term ...3,11,31,69,131

1^3+2=32^3+3=113^3+4=314^3+5=69

5^3+6=131

therefore 6^3+7=223

sct sample paper

Documents