TCS Aptitude Paper December 2010

Posted on :18-01-2016

Q1. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, it gets filled up like, 10, 20, 40,80, 160..in tank B. 1/8 th of the tank B is filled in 22 hours. What is the time to fill the tank fully?

(a) 26

(b) 25

(c) 5

(d) 27

ANS: 25

Explanation:

Tank B is filled in geometric progression, so after 22 hrs water in tank will be = 10 * 2^21 = x/8 

where x = volume of tank x = 10 * 2^24 thus by geometric progression we get that n-1 = 24 

so n = 25, hence time required is  25 hrs.

 

Q2. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says At least n of the statements on this sheet are false.Which statements are true and which are false?

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

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

(c) The first 35 statements are true and the last 35 are false.

(d) The first 35 statements are false and the last 35 are false.

ANS: C

Explanation:

 Note: For this type of Questions, follow this:

–At least- Ist half are true, Last half are false

–Exactly- Last second one is true or (N-1)th Statement is true

–Almost- All are true.

 Aliter : 

Suppose the first 35 statements are true!

Statement 1: At least 1 statement is false [TRUE]

Statement 2: At least 2 statements are false   [TRUE]

Statement 35: At least 35 statements are false  [TRUE]

——————————————————————–

Statement 36: At least 36 statements are false  [FALSE]

..

Statement 40: At least 40 statements are false  [FALSE]

——————————————————————-

AT LEAST puts the minimum tag or the floor tag on the statements

So, if the first 35 statements are true and the rest are false, everything fits into place! 

 

Q3. Unnecessary data. A lady has fine gloves and hats in her closet- 18 blue- 32 red , 10 white , 25 yellow, 55 purple, 30 orange. The lights are out and it is totally dark in spite of the darkness. She can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color of blue, red, yellow?

         (a) 59

(b) 8

(c) 50

(d) 42

ANS: a(32+25+2)

Explanation:

Note: For this type of questions:

Bigger+Middle+1 (Suppose 18, 32, 25 =32+25+1), If you do not find answer in options, choose the one closer those the answer you got.

 

 

Q4. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the same 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 in total?

For this type question you should follow d step of basic math that will helpful you get enough time from  that.

12 prog 12 line 12 min

1 prog 12 line 12*12

1 1 12*12/12

72 1 12*12/(12*72)

72 72 12*12*72/(12*72)

ANS12

         Explanation:

Note: This question appears 3 times in our question but app is different please follow basic rule think it it is very very easy.

 

Q5. 12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3},  {a11, a12}, {a12, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

(a) 12

(b) 4

(c) 18

(d) 11

ANS: A

Explanation:

12 x 11 / 2 = 66 Handshakes

 

Q6. 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 each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true?

A. All suspects are lying.

B. leftmost suspect is innocent.

C. leftmost suspect is guilty

         (a) A only

(b) A or C

(c) A or B

(d) B only

ANS: C

Explanation:

Here leftmost person is lying since there is nobody to his right!-U have to visualise the rightside of the person and not yours!

Ans is c . Here leftmost person is lying since there is nobody to his right!-

you have to visualise the rightside of the person and not yours!

< 1< 2< 3< 4< 5< 6< 7< 8< 9< 10 this is there right side they are facing u..10th right most of you not questioned left most of u is 1 he is guilty as he is saying that the person to his right is guilty but there is no one to his right and first statement is false as 2 is not lying as 1(left most of u) is guilty as 1 is guity then not innocent so neither of them  

 

Q7. Alok and Bhanu play the following min-max game. Given the expression N = 15 + 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 this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to 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 the game would be?

ANS: 15+18 =33

 

Q8. How many four digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4? Can you help Alok find the answer?

(a) 100

(b) 125

(c) 75

(d) 85

ANS: 5^n-i

Explanation:

1= 5^4-1=125, n= no of digits

 

—  — 1 2

— — 2 4

— — 3 2

— — 4 4

— — 5 2

The first two digits in the place can be filled in 5 x 5 ways.

So there are totally 25 x 5 = 125 ways

 

Q9. The age of the two friends were in the ration of 6:5.If the sum of their ages is 66.Then after how many years their ratio will become 7:6?

a)11 

b) 6 

c) 10 

d) 12

ANS: 6

Explanation:

Let the age of two friends be 6x and 5x

Sum of their ages 66 => 6x + 5x = 66 => 11x = 66 => x=6

The ages will be 36 and 30

 (36+k)/(30+k) = 7/6 => 36 x 6 + 6k = 210 + 7k

216 + 6k = 210 + 7k => 6 = k

After 6 years their ages will be in the ratio 7:6

 

Q10. The age of the two friends were in the ratio of 2:3.If the sum of their ages is 55.Then after how many years their ratio will become 4:5? 

a) 11                           

b) 33                          

c) 22               

d) 44

ANS: 22

Explanation:

Let the age be the friends be 2x and 3x. Sum of their ages = 55

2x + 3x = 55 => 5x=55 => x=11

Their ages are 22 and 33

After k years both of them will be 22+k and 33+k years old

Ratio of their age at that time will me 4:5

  • (22+k)/(33+k)=4/5 
  • 5(22+k)=4(33+4) => 110 + 5k = 132+4k
  • K=132-110 = 22

Q11. A volume of 10936 l water is in a container of sphere.How many semisphere of volume 4l each will be required to transfer all the water into the small semispheres?

a) 2812                       

b) 8231                       

c) 2734                       

d) 4222

ANS: 2734

 

Q12. A person is manufacturing a house. He bought 20 ropes of wire which has a density of 300 Kg/m3.The height of the building to be constructed is 40 m. If the capacity of the current passed in the wire is 20 A and the voltage capacity is 80 Volts.Then what will be the opposing force to the current if the wire is used ?

a) 2 
b) 4
c) 8                             

d) 1600
 
ANS: 4

Explanation:

by ohms law 

v = ir 

so r = v/i 

so r = 80/20 = 4   

 

Q13. A horse chases a pony 2 hours after the pony runs. Horse takes 3 hours to reach the pony. If the average speed of the horse is 81Kmph.Then what is the average speed of the pony?

a) 46.4
b) 51
c) 53.4                        

d) 48.6
 
ANS: 48.6

Explanation:

Horse covers = 81*3 = 243 kms

So ponys speed = 243/(2+3) = 243/5 = 48.6

 

Q14. The difference between two no is 9 and the product of the two is 14.What is the square of their sum?

a)120              

b)130              

c)137              

d)145

Explanation:

One number be x and other y, then  x – y = 9

(x – y)2 = 81

x2 + y2 = 81 + 2xy = 109

(x+y)2 = x2 + y2 + 2xy = 109 + 28 = 137

So answer is 137

 

Q15) 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 of this 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 the solar blast.Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?

         a) 15
         b) 21.25 

c) 12.25 
d) 14.05
 
ANS: 15

Explanation:

d = 4*(t-9)

Given r = 12 mm

So, d = 24 mm

So,

24 = 4t – 36

4t = 60

t = 15 years  

Q16. A man goes 50Km north , then turned left walked 40Km, then turned right ? In which direction he is?

a) North                      

b) South                     

c) East                        

d) West

ANS: North

Explanation:

Left and right consecutive movement nullified the change in direction. So, he is in the direction he started with. 

 

Q17. In T. Nagar the building were numbered from 1 to 100.Then how many 6s will be present in the numbers?

a) 18 

b) 19 

c) 20 

d) 21

ANS: 20

 

Q18. 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 sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has employed great success .Rohit once bought a Ferrari. It could go 4 times as fast as Mohans old Mercedes. If the speed of Mohans Mercedes is 35 km/hr and the distance traveled by the Ferrari is 490 km, find the total time taken for Rohit to drive that distance.

a) 7/2
b) 9/2
c) 238.25 
d) 6.18
 
ANS: 7/2

Explanation:

Mohans speed = 35 Km/hr

Rohit speed = 4 x Mohan speed = 4 x 35 = 140 Kmph

Time taken =Distance / Speed = 490 / 140 = 49/14 = 7/2

 

Q19. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says  At least n of the statements on this sheet are false. Which statements are true and which are false?

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

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

c) The first 35 statements are true and the last 35 are false.

d) The first 35 statements are false and the last 35 are false.

 

Q20. A man goes north 37km. turns left goes 2km.turns right goes 17km.turns right goes 2km. find distance b/w starting ending point.

a) 54 
b) 27 
c) 81 
d) 67 
 
ANS: 54

Explanation:

Distance between the starting and end point is 37 + 17 = 54

 

Q21. If there are 30 cans out of them one is poisoned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisoned can?

a) 3                             
b) 2                             
c) 6                             
d) 1 
ANS: 5

Explanation:

Have 6 mice for testing,

Give each mice contents from 5 cans each

5 5 5 5 5 5

After 14 hours, one of the mice will die

So, we will know which 5 cans must have the poison

Then , take the contents of these 5 cans and give to the remaining 5 mice each.

We will know in due time which can is poisoned

5C1+5C2+5C3+5C4 = 5 + 10 + 10 + 5 = 30

 

Q22. If a and b are mixed in 3:5 ration and b and c are mixed in 8:5 ration if the final mixture is 35 liters, find the amount of b?

a) 13.34 
b) 15.73 
c) 16.73 
d) 9.45
 
ANS: 15.73

Explanation:

a: b = 3:5

b: c =   8: 5

a:b:c  = 24 : 40 : 25  and total is 24+40+25 = 89 

(40/89) x 35 = 15.73

Q23. It is the class with the seating arrangement in 4 rows and 8 columns. When the teacher says start the girl who is sitting in first row and first column will say 1, then the next girl sitting behind her will say 4, the next girl sitting behind that girl will say 7, in a particular order each girl is telling a number, the following girls told 10, 13 next turn is yours what u will say? 

a) 15                

b) 17               

c) 14               

d) 16 

ANS: 16

 

Q24. It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color?

a) 2                 

b) 3                             

c) 48               

d) 25

ANS: 25

 

Explanation:

The Answer is 25. First he will select 24 in that the maximum chance is all are redm so if we take one more socks, it has to be the other color. Hence, the answer is 24 + 1 = 25

 

Q25. If the Valentines Day in 2005 falls on Monday, then on which day will the Valentines Day fall on 2010?

a) Saturday   
b) Thursday    
c) Wednesday 
d) Sunday
 

ANS: Sunday

 

Explanation:

FEB. 14, 2005   IS A  MONDAY
From Feb. 14, 2005 to Feb. 14 2006, there will be 365 days which means one odd day. 
So, FEB. 14, 2006   WILL BE A  TUESDAY
From Feb. 14, 2006 to Feb. 14 2007, there will be 365 days which means one odd day. 
So, FEB. 14, 2007   WILL BE A  WEDNESDAY 
From Feb. 14, 2007 to Feb. 14 2008, there will be 365 days which means one odd day. 
So, FEB. 14, 2008   WILL BE A  THURSDAY 
From Feb. 14, 2008 to Feb. 14 2009, there will be 366 days
– add one more odd day for Feb.29. Total is 2 odd days. 
So FEB. 14, 2009    WILL BE A  SATURDAY
From Feb. 14, 2009 to Feb. 14 2010, there will be 365 days
one  odd day . 

So FEB. 14, 2010    WILL BE A  SUNDAY

Q27. An athlete decides to run the same distance in 1/4th less time that she usually took. By how much percent will she have to increase her average speed?

a) 40 

b) 44.4 

c) 33.3 

d) 22.2

 
ANS: 33.3

Explanation:

(3/4)t=1

t=4/3=1+1/3

She will have to increase her speed by 33.333% to run the same distance in 3/4s of the time.. 

 

Q28. In a building there are 5 rooms. Each having a equal area .The length of the room is 4m and bread ht is 5 m.The height of the rooms are 2m.If 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room?

a) 6460           
b) 3080              
c) 3640              
d) 3080
 
ANS: 6460

Explanation:

Dimensions = 4 x 5 x 2

TSA = 2 (4 x 5 + 5 x 2 + 4 x 2) = 2(20+10+8)=2×38 =  76 sq m

So bricks required = 76 x 17 = 1292

For 5 rooms 1292 x5 = 6460

 

Q29. One man want to build a wall .The length and breadth of the wall are 20 and 30 respectively. He need 35 bricks for one square centimeter then how many bricks he need?

a) 21,500                    

b) 30,000                    

c) 21,000        

d) 20,000
 
ANS: 21000

Explanation:

Area = 20 x 30 = 600 cm^2

 Bricks = 600 x 35 = 21000

 

Q30. In a hotel we can order two types of varieties,but we can make 6 more varieties in home.One can choose the four varieties with two from hotel as must.Find how many ways one can order.

a) 14               
b) 15               
c) 56              
d) 28
 
ANS: 15

Explanation:

No of ways of selecting 2 from hotel (6 choices) = 6C2

And from home (2 choices) = 2C2 

 2C2 x  6C2  = 1 x 15 = 15 ways

 

Q31. If a pipe can fill the tank within 6hrs. But due to leak it takes 30 min more.Now the tank is full then how much time will it take to empty the tank throught the leak.?

a) 78               
b) 56               
c) 66              
d) 59
 
ANS: 78

Explanation:

Let the capacity of the tank be 6 litre.

Then time to fill this tank is 6 hour ,when there is no leakage .

so in 1 hour it fills 1 litre.

when leakage is there then it takes 6.5 hour to fill 6 litre 

so in 1 hour it fills 6/6.5 litre.

Time to vacate will be 1-(6/6.5) = 1/13 litre in 1 hour

time to vacate 1 litre will be 13 hour.

For 6 litre it will be 13*6 =78 

 

Q32. The bacteria has the probability of split into 3 and probability to die is 1/3rd of the total bacteria.Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?

a) P=1/3+1/5*3 
b) P=1/5*(1/8-3)
c) p = (1/3) + (3* 1/5) 
 
ANS: c) p = (1/3) + (3* 1/5) 

Explanation:

Probability for the bacteria to be dying = 1/3

Hence probability of survival = 1/5

if they survive, they will be split into 3 more bacteria hence, p = (1/3) + (3* 1/5) 

 

Q33. There is a bacteria which has the probability of die 1/3 of its total number or it may tripled. Find out the probability

A. P=1/3+(2/3*p^3) 

B. P=2/3+(2/3*p^3) 

C. P=2/3+(1/3*p^3) 

D. P=2/3+(2/3*p^3)
 
ANS: A. P=1/3+(2/3*p^3) 

 Explanation:

Probability of bacteria to die is 1/3

or its get tripled, hence the probability of getting tripled is (2/3)*p*p*p that is  (2/3)*p^3

so both the probability combined as P=1/3+(2/3*p^3)

Q34. Amrith told to Anand in front of a Photo that He is the son of my fathers son.Find who is in the picture if amrith have no brothers and sisters.

a) Amrith himself 

b) Amriths Uncle 

c) Amriths Father 

d) Amriths son

ANS: Amriths son

 

Q35. One person has no siblings and says, the guy in the photo is the only son of my father s son. What is the relation of the guy to the person?

ANS: Son

 

Q36. One grand father has 3 grand children two of the age difference is 3.Eldest child age is 3 times the youngest childs age and the eldest child age is two year more than the sum of other two children. Find what is the age of the elders child?

a) 8 
b) 12 
c) 30 
d) 10
 
ANS: 8

Explanation:

Let the age of eldest child is E , that of elder child is M and that of youngest child is Y, then according to the given conditions

 

E = 3Y  (1) and  E = 2 + M + Y  (2)

Third condition is somewhat complicated, according to this condition two of the age difference is 3 so three cases will arise 

1) E – M = 3, ……(3)

2) M – Y = 3, ……(4)

3) E – Y = 3, ……(5)

 

if we take first of the 3 conditions then on solving (1), (2) and (3) we will get E = 3, M = 0, Y = 1 which is wrong now on solving (1), (2) and (4) we will get E = 15, M = 8, Y = 5

similarly on solving (1), (2) and (5) we will get E = 4.5, M = 1, Y = 1.5

only E = 15, M = 8, Y = 5 is correct so age of elder child is 8 years