Quant Questions

1

A man earns x% on the first Rs. 2,000 and y% on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from if his income is Rs. 5,000, find x%.

  1. 10%
  2. 15%
  3. 20%
  4. 25%
2

How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

  1. 4 years
  2. 4.5 years
  3. 5 years
  4. 5.5 years
3

A certain sum of money invested at some rate of simple interest triple itself in 4 years. In how many years the principal will become 9 times of itself at the same rate?

4

In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having either cable TV or VCR?

  1. 23/30
  2. 2/3
  3. 17/30
  4. 19/30
5

In a certain village, 22% of the families own agricultural land, 18% own a mobile phone and 1600 families own both agricultural land and a mobile phone. If 68% of the families neither own agricultural land nor a mobile phone, then the total number of families living in the village is

  1. 20000
  2. 10000
  3. 8000
  4. 5000
6

A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?

  1. 6666666
  2. 6666600
  3. 6666660
  4. 6666000
7

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees?

  1. 80
  2. 160
  3. 200
  4. 320
8

Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?

  1. 4
  2. 6
  3. 8
  4. 10
9

Boxes numbered 1, 2, 3, 4 and 5 are kept in a row, and they which are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?

  1. 8
  2. 10
  3. 15
  4. 22
10

How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?

  1. 0
  2. 1
  3. 3
  4. 4
11

In a six-node network, two nodes are connected to all the other nodes. Of the remaining four, each is connected to four nodes. What is the total number of links in the network?

  1. 7
  2. 13
  3. 15
  4. 26
12

In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the the vice chairman and a director?

  1. 9! × 2
  2. 2 × 7!
  3. 2 × 8!
  4. 2 × 6!
13

Let S be the set of five-digit numbers formed by digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd position are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S?

  1. 192
  2. 216
  3. 228
  4. 294
14

Ten points are marked on a straight-line and 11 points are marked on another straight-line. How many triangles can be constructed with vertices from among the above points?

  1. 495
  2. 550
  3. 1045
  4. 2475
15

There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

  1. 144
  2. 180
  3. 192
  4. 360
16

What is the number of distinct terms in the expansion of (a + b + c)20?

  1. 210
  2. 231
  3. 242
  4. 253
17

During the essay writing stage of MBA admission process in a reputed B-School, each group consists of 10 students. In one such group, two students are batch mates from the same IIT department. Assuming that the students are sitting in a row, the number of ways in which the students can sit so that the two batch mates are not sitting next to each other, is

  1. 3540340
  2. 2874590
  3. 2903040
  4. None of the above
18

In the board meeting of a FMCG Company, everybody present in the meeting shakes hand with everybody else. If the total number of handshakes is 78, the number of members who attended the board meeting is

  1. 7
  2. 9
  3. 11
  4. 13
19

There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% student play both the games. What is the number of students who play neither cricket nor football?

  1. 25
  2. 20
  3. 18
  4. 15
20

Out of 120 applications for a post, 70 are male and 80 have a driver's license. What is the ratio between the minimum to maximum number of males having driver's license?

  1. 2 to 3
  2. 3 to 7
  3. 1 to 2
  4. 5 to 7
21

Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively.

Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?

  1. 0.004
  2. 0.006
  3. 0.216
  4. 0.994
  5. 0.996
22

If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed?

  1. 1/12
  2. 1/6
  3. 1/8
  4. 1/4
23

An unbiased dice is thrown. What is the probability of getting

  • (i) an even number
  • (ii) a multiple of 3
  • (iii) an even number or a multiple of 3
  • (iv) an even number and a multiple of 3
24

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is:

  • (i) an ace
  • (ii) red
  • (iii) either red or king
  • (iv) red and a king
25

There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B. If a bag is selected at random and a ball is selected from that, what is the probability that it is red?

26

The internal evaluation for Economics course in an Engineering programme is based on the score of four quizzes. Rahul has secured 70, 90 and 80 in the first three quizzes. The fourth quiz has ten True-False type questions, each carrying 10 marks. What is the probability that Rahul’s average internal marks for the Economics course is more than 80, given that he decides to guess randomly on the final quiz?

  1. 12/1024
  2. 11/1024
  3. 11/256
  4. 12/256
27

A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?

  1. 5/36
  2. 8/36
  3. 15/36
  4. 21/36
  5. None of the above
28

Consider the system of linear equation

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

The system has

  1. Infinite no. of solutions
  2. No solution
  3. Unique solution
  4. Exactly 3 solutions
29

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:

  1. 7
  2. 13
  3. 14
  4. 18
30

Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

  1. 5
  2. 9
  3. 11
  4. 15
31

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r ≠ 0?

  • x + 2y - 3z = p
  • 2x + 6y - 11z = q
  • x - 2y + 7z = r
  1. 5p - 2q - r = 0
  2. 5p + 2q + r = 0
  3. 5p + 2q - r = 0
  4. 5p - 2q + r = 0
32

If x and y are integers, then the equation 5x + 19y = 64 has

  1. A solution for -59 < y < -56
  2. No solution for x > 250 and y > -100
  3. A solution for 250 < x < 300
  4. No solution for x < 300 and y < 0
33

Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

  1. 17
  2. 18
  3. 19
  4. 20
34

What is the value of k for which the following system of equations has no solution: 2x –- 8y = 3 and kx + 4y = 10.

  1. 2
  2. -2
  3. -1
  4. 1
35

Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas and one apple cost Rs.10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?

  1. Rs 8
  2. Rs 10
  3. Rs 12
  4. Rs 15
36

In 2004, Rohini was thrice as old as her brother Arvind. In 2014, Rohini was only six years older than her brother. In which year was Rohini born?

  1. 1984
  2. 1986
  3. 1995
  4. 2000
37

A firm is thinking of buying a printer for its office use for the next one year. The criterion for choosing is based on the least per-page printing cost. It can choose between an inkjet printer which costs Rs. 5000 and a laser printer which costs Rs. 8000. The per-page printing cost for an inkjet is Rs. 1.80 and that for a laser printer is Rs. 1.50. The firm should purchase the laser printer, if the minimum number of a pages to be printed in the year exceeds

  1. 5000
  2. 10000
  3. 15000
  4. 18000
38

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

  1. 5 years
  2. 6 years
  3. 7 years
  4. 8 years
  5. 9 years
39

In the figure given, LM is parallel to QR. If LM divides the triangle PQR such that area of trapezium LMRQ is two times the area of triangle PLM, then what is PL/PQ equal to?

  1. 1/3
  2. 1/√2
  3. 1/√3
  4. 1/2
40

A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is

  1. 5√3 cm
  2. 5 cm
  3. 10√3 cm
  4. 10 cm
41

If A, B, C, D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D equal to?

  1. 0
  2. 1
  3. 2
  4. 4
42

What is the length of the perpendicular drawn from the centre of circle of radius r on the chord of length √3r?

  1. r/4
  2. r/2
  3. √2r
  4. r
43

ABC is an isosceles triangle such that AB = BC = 8 cm and ∠ABC = 90°. What is the length of the perpendicular drawn from B on AC?

  1. 4√2 cm
  2. 4 cm
  3. 2 cm
  4. 2√2 cm
44

In the figure given, ∠B = 38°, AC = BC and AD = CD. What is ∠D equal to?

  1. 26°
  2. 28°
  3. 38°
  4. 52°
45

How many degrees are there in an angle which equals two-third of its complement?

  1. 60°
  2. 48°
  3. 45°
  4. 36°
46

ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Consider the following statements:

  1. Triangles ADX and BAY are congruent
  2. ∠DXA = ∠AYB
  3. DX is inclined at an angle 60° with AY
  4. DX is not perpendicular to AY

Which of the above statements are correct?

  1. 2, 3 and 4 only
  2. 1, 2 and 4 only
  3. 1, 3 and 4 only
  4. 1 and 2 only
47

In the figure given below, M is the mid-point of AB and ∠DAB = ∠CBA and ∠AMC = ∠BMD. Then the triangle ADM is congruent to the triangle BCM by

  1. SAS rule
  2. SSS rule
  3. ASA rule
  4. AAA rule
48

In the figure given below, ABC is a triangle with AB = BC and D is an interior point of the triangle ABC such that ∠DAC = ∠DCA.

 

Consider the following statements:

  1. Triangle ADC is an isosceles triangle.
  2. D is the centroid of the triangle ABC.
  3. Triangle ABD is congruent to the triangle CBD.

Which of the above statements are correct?

  1. 1 and 2 only
  2. 2 and 3 only
  3. 1 and 3 only
  4. 1, 2 and 3
49

In the figure given below, PQ is parallel to RS and PR is parallel to QS, If ∠LPR = 35° and ∠UST = 70°, then what is ∠MPQ equal to?

  1. 55°
  2. 70°
  3. 75°
  4. 80°
50

In the figure given below, PQR is a non-isosceles right-angled triangle, right angled at Q. If LM and QT are parallel and QT= PT, then what is ∠RLM equal to?

  1. ∠PQT
  2. ∠LRM
  3. ∠RML
  4. ∠QPT