# TCS Aptitude Test 3

## Question No : 1

Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 31, the number of points equidistant from all the 3 lines is

 A. 3 B. 4 C. 0 D. 1
##### Explanation
Discuss the solution
• The answer is option B.
There are 4 such points. One point is the incenter of the triangle.
3 are the excenters with respect to each angle of the triangle. In the picture given,
below I is the Incenter and JA, JB, JC are excenters.

## Question No : 2

For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazingsuccess. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A’schances of winning.Let’s assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger teamhas a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner ofthe Ghana-Bolivia game?

 A. 4/9 B. 2/3 C. 1/9 D. 5/9
##### Explanation
Discuss the solution
• Paul picks A with the same probability as A’schances of winning
So probability of picking a winner = prob picking of ghana * ghana winning + prob picking of bolivia * bollivia winning
= 2/3 * 2/3 + 1/3 * 1/3
= 5/9

## Question No : 3

A result of global warming is that the ice of some glaciers is melting. 12 years after the ice disappears, tiny plants, called lichens, start to grow on the rocks. Each lichen grows approximately in the shape of a circle. The relationship between the diameter of this circle and the age of the lichen can be approximated with the formula: d =5* (t -12) for t >12, where d represents the diameter of the lichen in millimeters, and t represents the number of years after the ice has disappeared. Using the above formula, calculate the diameter of the lichen, 49 years after the ice has disappeared.

 A. 702 B. 468 C. 13 D. 689
##### Explanation
Discuss the solution
• d=18(t-13)
put t=39
d=468mm

## Question No : 4

Alok is attending a workshop 'How to do more with less and today's theme is Working with fewer digits. The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as womankind) had only worked with fewer digits. The problem posed at the end of the workshop is 'How many 5 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
##### Explanation
Discuss the solution
• The chances for last two digits:{(1,2);(2,4);(3,2);(4,4)[because with repetition];(5,2)} there are totally five chances

The chances for 1st and 2nd digit chances same 5 digits (1,2,3,4,5) because with repetition then the probaility of 1st two digit is=5*5

Then the total probability =(5*5)*(5)=125

## Question No : 5

Elephant competitions are of great entertainment value in south India. In one such competition held in Cochin, 200 elephants participated. Each elephants was given equal amount of milk to drink for a certain time period. Whichever elephant could drink the maximum would be the winner. One of the elephants named Garru could drink 1/3 of the amount of milk offered. Another elephant named Marta could drink only 1/20 of the amount of milk offered, but it was better than Thorny which could drink 2/45 of the amount of milk offered. Amazingly Darru could drink 6 litres more than 1/4 of the amount of milk offered, where as Malar could drink 2/15 of the amount of milk offered. If the amount of milk left over by the elephants Garru and Darru were same, then calculate the total amount of milk offered to each elephant.

 A. 73 B. 72 C. 71 D. 70
##### Explanation
Discuss the solution
• let each elephant was given 'x' litres of milk.
now according to ques.
garru drink = x/3L & darru drink = 6+x/4L
it means milk left by,
garru = [x-x/3] & darru = [x-(6+x/4)]
again acc to ques.
[x-x/3] = [x-(6+x/4)]
on solving we get 'x' = 72L

## Question No : 6

Planet Fourfe resides in 4-dimensional space and thus the currency used by its residents are 3- dimensional objects. The rupee notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins. A. The diamere of the coins should be at least 16 mm and not exceed 64mm.B. given a coin the diameter of the next larger coin is at least 50% greater.C. the diameter of the coin must always be an integer.You are asked to design a set of coins of different diameters with their requirements and your goal is to design as many coins as possible. How many coins can you design?

 A. 6 B. 2 C. 4 D. 3
##### Explanation
Discuss the solution
• ans is 4 coins.
first coin would be of 16 diameter.
50%of 16 is 8, 8+16=24mm of diameter (second coin)
50%of 24 is 12, 24+12=36mm (third coin)
50%of 36 is 18, 36+18=54mm (fourth coin)
now, 50%of 54 is 27, 27+54=81 > 64mm. hence it will not be included.
therefore 16mm,24mm,36mm,54mm

## Question No : 7

The citizens of planet Oz are 4 fingered and thus have developed a number system in base 4. A certain street in Oz contains 100 buildings numbered from 1 to 100. How many 1's are used in numbering these buildings? Express your answer in base 10.

 A. 5 B. 8 C. 4 D. 12
##### Explanation
Discuss the solution
• in the question they have mentioned it as "base 4", so we should take numbers from from 0 to 4, so take the number series as:
0,1,2,3,4,
11,12,13,14,
21,22,23,24,
31,32,33,34,
41,42,43,44, hence in abv series ter are 8 2s.
(since the base is 4 consider the number series only till 40's.
if base 8 then consider till 80's and so on........)
or the question can also be solved by using formula.... 2*n ==> 2*4=8

## Question No : 8

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 ans also write code at the same rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many lines of code can be written by 72 programmers in 72 minutes?

 A. 72 B. 432 C. 14 D. 144
##### Explanation
Discuss the solution
• Applying Man*Days=Work forumla.
Assuming P=Programmer, T= Time in minutes and C= Line of codes

12P*12T=12C (Equtation 1)
72P*72T = x Lines of Code
6*6(12P*12T) = x (Equtation 2)
Replacing 12P*12T=12C from equation 1 above in Equtation 2
We get 6*6(12C) =x
So x = 432 C

Hence answers is b) 432 lines of Code

## Question No : 9

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.
##### Explanation
Discuss the solution
• This question is based on at least, so truth of any statement (suppose nth) will imply the truth of all (n-1)th, (n-2)th,....... 1st statements, so the only possible answer will be c) The first 35 statements are true and the last 35 are false.

## Question No : 10

For the King's revelry 254 barrels of beer have been ordered. However, it was found that one of them is poisoned. The poison takes effect even if consumed in the tiniest amount after 14 hours. You need to find, within 24 hours, the poisoned barrel and have at your disposal some beer guzzling mice. The smallest number of mice required to find the poisoned barrel is

 A. 9 B. 8 C. 254 D. 7
##### Explanation
Discuss the solution
• 2^8=256>254
so the ans is 8.
becoz in the option here 1 is not given,if 1 is given then 1 will be the correct ans.

## Question No : 11

Doller stores, the stores which sell all of their merchandise for \$1, have long had a reputation for being down at the heels places to buy cheap, generic goods. While keeping their low prices, they are revamping their image and climbing the respectability ladder, in some cases to the fortune 500. One such dollar store which recently made an entry in the fortune list which has 2500 stores all over the United States said that they had a 2 percent increase in the number of transaction in 2008 compared with the previous year to 37 million. The company made a profit of \$20 million this year. What is the average profit per store?

 A. 8000 \$ B. 9000 \$ C. 10000 \$ D. 7000 \$
##### Explanation
Discuss the solution
• Per store profit = 20/2500 million \$ = 2/250 million \$ = 0.008*1000000 \$ = 8000 \$

## Question No : 12

Mr. Beans visited a magic shop and bought some magical marbles of different colours along with other magical items. While returning home whenever he saw a coloured light, he took out marbles of similar colours and counted them. So he counted the pink coloured marbles and found that he has bought 25 of them. Then he counted 14 green marbles and then 21 yellow marbles. He later counted 30 purple coloured marbles with him. But when he reached a crossing, he looked at a red light and started counting red marbles and found that he had bought 23 Red marbles. As soon as he finished counting, it started raining heavily and by the time he reached home he was drenched. After reaching home he found that the red, green and yellow marbles had magically changed colours and became white, while other marbles were unchanged. It will take 1 day to regain its colours, but he needs to give atleast one pair of marbles to his wife now. So how many white marbles must be choose and give to his wife so as to ensure that there is atleast one pair of red, yellow and green marbles ?

 A. 46 B. 35 C. 25 D. 48
##### Explanation
Discuss the solution
• The problem is solved assuming worst case situation(all consecutive marbels of same colour) and here the numbers must be initiated from majority,ie
23 for red
next 21 for yellow
remaining two for yellow
total 23+21+2=46

## Question No : 13

A police car starts chasing a fugitive in a BMW 3 hours after the BMW escapes from the scene of crime at 10AM.The BMW drives for 10Km through the crowded roads of Shanghai and then drives into a highway,where the traffic allows vehicles to move twice as fast.After a while,the police car finally catches up with BMW after a chase that lasted 4 hours.By this time the moon was up in the sky for 4 hours.If the average speed of the police car is 83 kmph,then the average speed of the BMW is .....kmph

 A. 35.2 B. 25.7 C. 47.43 D. 42.23
##### Explanation
Discuss the solution
• Distance covered by police is 4*83=332km.
The Fugitive covered the same distance in 4+3=7 hours.
so, the avg. speed of BMW is 332/7=47.43kmpph.

## Question No : 14

19 people (a1, a2, ….. , a19) are invited to a party. The host and the hostess shake hands with each invitee and also with each other. The invitees shake hands in a circular fashion, i.e. the pairs (a1, a2), (a2, a3), ……..,(a18, a19), (a19, a1) shake hands. So, in all there are 58 handshakes. Let S be a set of people such that every pair in S shake hands. The size of S is at most

 A. 2 B. 3 C. 1 D. 4
##### Explanation
Discuss the solution
• 4 persons
Any pair of 2 persons, host, hostess

## Question No : 15

A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 1 face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

 A. 900 B. 563 C. 488 D. 592
##### Explanation
Discuss the solution
• total number of blocks=(5*5*5)-(3*3*3)=98
so total no of faces of smaller cubes=98*6=588
and among all these faces one face of bigger cube is painted so totally 25 faces of small cubes r painted
it means total unpainted faces=588-25=563

## Question No : 16

Anoop managed to draw 5 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side.Find the ratio of the the side of the square to radius of the circles. You may assume that square root of 2 is 1.4

 A. 2.2 B. 3 C. 8.9 D. 7.6
##### Explanation
Discuss the solution
• Let the radius of circle be r
let the side of square be a
then diagonal of square= a*sqrt(2)
This diagonal length = 8*r + 2r * sqrt(2)
(because the extreme circle's radius is perpendicular to side of square.)
Thus we get

8*r+2r*sqrt(2)=a*sqrt(2)

r(4*sqrt(2)+2)=a
so a/r=(4*sqrt(2)+2)/1
Thus ratio: a:r =(4*sqrt(2)+2)/1
= 7.6
Ans: 7.6

## Question No : 17

Subha Patel is an olfactory scientist working for International Flavors and Fragrances. She specializes in finding new scents recorded and reconstituted from nature thanks to Living Flower Technology. She has extracted fragrance ingredients from different flowering plants into bottles labeled herbal, sweet, honey, anisic and rose. She has learned that a formula for a perfume is acceptable if and only if it does not violate any of the rules listed: If the perfume contains herbal, it must also contain honey and there must be twice as much honey as herbal. If the perfume contains sweet, it must also contain anisic, and the amount of anisic must equal the amount of sweet. honey cannot be used in combination with anisic. anisic cannot be used in combination with rose. If the perfume contains rose, the amount of rose must be greater than the total amount of the other essence or essences used. Which of the following could be added to an unacceptable perfume consisting of two parts honey and one part rose to make it acceptable?

 A. Two parts rose B. One part herbal C. Two parts honey D. One part sweet
##### Explanation
Discuss the solution
• a) 2 parts of rose
reason:
one part of herbal cant be used because it has to be of double quantity as that of honey
two parts of honey can not be used as it will increase the qty of honey than rose
and lastly one part of sweet can nto be used because sweet must be used in combinatoin with anisic which in turn is incompatible with rose.

Hence option a is the answer

## Question No : 18

A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has coverd 1/4 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance.By what factor should the hare increse its speed so as to tie the race?

 A. 25 B. 35 C. 22 D. 37
##### Explanation
Discuss the solution
• Diameter of the circle = 100 yards
thus perimeter of the circle is 100*3.14 yards
distance covered by tortoise when both meet =7/8 of total
speed of hare is 1/8of total per unit
and speed of tortoise is 5/8 of total per unit of time
to tie the race hare should complete 7/8 of total distance in the time tortoise completes 1/8 of total distance
time taken by tortoise to complete 1/8 of total distance =1/5unit of time
required speed of hare =35/8of total distance per unit of time
thus hare should increase its speed 35 times to tie the race

## Question No : 19

45 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 the suspects are lying. B. The leftmost suspect is guilty.C. The rightmost suspect is guilty.

 A. B only B. A only C. A and B D. A and C
##### Explanation
Discuss the solution
• ans: A and B
If right most suspect is guilty, the last but one person is saying truth which is controversial to A. see that B satisfies A. So A and B are ans.

## Question No : 20

A circular dashboard of radius 2.0 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?

 A. 0.25 B. 0.75 C. 1 D. 1.5
##### Explanation
Discuss the solution
• for the point to be closer to the centre it cshould lie within the area of 1ft radius of the board
so probability=(1^2)/(2^2)=.25

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