# TCS Aptitude Practice 1

## TCS Aptitude Test 1

This is the

**First Test**in the series "**Practice TCS Aptitude Test**". Please remember that you have to**make exam environment by yourself**. You can take the test as many times as you wish.*You may expect lots of questions from this Test with different data in your real Aptitude Test.*:)**Best of Luck !**
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Question 1 |

The teacher is testing a student’s proficiency in arithmetic and poses the following question. 1/3 of a number is 3 more than 1/6 of the same number. What is the number? Can you help the student find the answer?

A | 12 |

B | 18 |

C | 6 |

D | 21 |

Question 2 |

If A, B and C are the mechanisms used separately to reduce the wastage of fuel by 30%, 20% and 10%. What will be the fuel economy if they were used combined?

A | 30% |

B | 20% |

C | 10% |

D | insufficient data |

Question 3 |

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

A | 4 |

B | 3 |

C | 0 |

D | 1 |

Question 4 |

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 |

Question 5 |

Anoop managed to draw 7 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 radius of the circles to the side of the square.

A | 1:(4+ 7v3) |

B | 1:(2+ 6v2) |

C | 1:(2+ 7v2) |

D | (2+ 7v2):1 |

Question 6 |

The pacelength P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed in kmph.

A | 23.62 |

B | 8.78 |

C | 11.39 |

D | 236.16 |

Question 7 |

Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P) over all configurations P of 10 points in the plane is

A | 5 |

B | 3 |

C | 9 |

D | 10 |

Question 8 |

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 woman kind) 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 | 375 |

B | 3125 |

C | 500 |

D | 625 |

Question 9 |

There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre 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 litres, second hour it has 20, and so on). If 1/32 of B’s volume is filled after 3 hours, what is the total duration required to fill it completely?

A | 9 hours |

B | 7 hours |

C | 8 hours |

D | 10 hours |

Question 10 |

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. |

Question 11 |

A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says “At most n of the statements on this sheet are false”. Which statements are true and which are false?

A | The odd numbered statements are true and the even numbered are false. |

B | The even numbered statements are true and the odd numbered are false. |

C | All statements are true. |

D | All statements are false. |

Question 12 |

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

A | The odd numbered statements are true and the even numbered are false |

B | The first 26 statements are false and the rest are true. |

C | The even numbered statements are true and the odd numbered are false. |

D | The first 13 statements are true and the rest are false. |

Question 13 |

Form 8 digit numbers from by using 1, 2,3,4,5 with repetition is allowed and must be divisible by 4?

A | 31250 |

B | 97656 |

C | 78125 |

D | 97657 |

Question 14 |

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

A | 3/4 |

B | 37/38 |

C | 1/2 |

D | 14/19 |

Question 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 1face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

A | 900 |

B | 488 |

C | 563 |

D | 800 |

Question 16 |

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

A | 5/9 |

B | 1/9 |

C | 2/3 |

D | 4/9 |

Question 17 |

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

A | 0 |

B | 12/212 |

C | 11/12 |

D | 1/12 |

Question 18 |

A lady has fine gloves and hats in her closet- 18 blue- 32 red and 25 black. The lights are out and it is totally dark inspite 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 colour?

A | 60 |

B | 50 |

C | 8 |

D | 42 |

Question 19 |

A and B play a game between them. The dice consist of colors on their faces(instead of number). When the dice are thrown, A wins if both show the same color, otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have if the both players have the same chances of winning?

A | 5 red and 1 blue faces |

B | 1 red and 5 blue faces |

C | 3 red and 3 blue faces |

D | wrong question |

Question 20 |

Entry ticket to an exhibition ranges from 1p to 31p. You need to provide exact change at the counter. You have 31p coin. In how many parts will you divide 31p so that you will provide the exact change required and carry as less coins as possible?

A | 21 |

B | 31 |

C | 6 |

D | 32 |

Question 21 |

A can do a piece of work in 20 days, which B can do in 12 days. In 9 days B does ¾ of the work. How many days will A take to finish the remaining work?

A | 5 |

B | 10 |

C | 15 |

D | 20 |

Question 22 |

A circular dartboard of radius 1 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 | 0.75 |

B | 1 |

C | 0.25 |

D | 0.5 |

Question 23 |

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 covered 1/5 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 increase its speed so as the win the race?

A | 8 |

B | 5 |

C | 37 |

D | 80 |

Question 24 |

Which is the smallest no divides 2880 and gives a perfect square?

A | 1 |

B | 2 |

C | 5 |

D | 6 |

Question 25 |

The citizens of planet Nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in Nigiet contains 1000 base buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?

A | 256 |

B | 54 |

C | 192 |

D | 108 |

Question 26 |

There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre 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 litres, second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?

A | 26 |

B | 25 |

C | 5 |

D | 27 |

Question 27 |

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

A | 33 |

B | 30 |

C | 28 |

D | 35 |

Question 27 Explanation:

15+18 = 35

Question 28 |

In the class of 40 students, 30 speak Hindi and 20 speak English. What is the lowest possible number of students who speak both the languages?

A | 5 |

B | 20 |

C | 15 |

D | 10 |

Question 29 |

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

A | 4 |

B | 3 |

C | 1 |

D | 0 |

Question 30 |

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 |

Question 31 |

The ratio of incomes of C and D is 3:4.the ratio of their expenditures is 4:5.Find the ratio of their savings if the savings of C is one fourths of his income?

A | 2:4 |

B | 1:4 |

C | 3:4 |

D | 4:5 |

Question 32 |

Horse started to chase dog as it relieved stable two hrs ago. And horse started to ran with average speed 22km/hr, horse crossed 10 mts road and two small pounds with depth 3m, and it crossed two small street with 200 mts length. After traveling 6 hrs, 2hrs after sunset it got dog. Compute the speed of dog?

A | 20Km/hr |

B | 16.5Km/hr |

C | 22.5Km/hr |

D | 18Km/hr |

Question 33 |

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

A | 6 |

B | 18 |

C | 72 |

D | 12 |

Question 33 Explanation:

(w1/w2=m1*t1/m2*T2)

Question 34 |

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 inspite 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 colour of blue, red, yellow?

A | 59 |

B | 8 |

C | 50 |

D | 42 |

Question 34 Explanation:

(32+25+2)

Question 35 |

In planet OZ planet there are 8 days, sunday to saturday and 8th day is OZ day. There is 36 hours in a day. What is angle between 12.40 ?

A | 80 |

B | 81 |

C | 87 |

D | 89 |

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