Quant Questions

1

If a - b = 4 and a2 + b2 = 40 where a and b are positive integers, where a and b are positive integers, then a3 + b6 is equal to

  1. 264
  2. 280
  3. 300
  4. 324
2

If the roots of the equation Ax2 + Bx + C = 0 are -1 and 1, then which one of the following is correct?

  1. A and B are both positive
  2. A and C are both negative
  3. A and C are of opposite sign
  4. A and C are both zero
3

The value of x2 - 4x + 11 can never be less than

  1. 7
  2. 8
  3. 11
  4. 22
4

Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are

  1. –4, –3
  2. 6, 1
  3. 4, 3
  4. –6, –1
5

If α and β are the roots of the equation x2 + px + q = 0, then what is α2 + β2 equal to?

  1. p2 – 2q
  2. q2 – 2p
  3. p2 + 2q
  4. q2 – q
6

Log (402 - 202) is equal to

  1. log 3
  2. log 60 + log 20
  3. log 40 – log 20
  4. log 20
7

If log25 5 = a and log25 15 = b, then the value of log25 27 is

  1. 3(b+a)
  2. 3(1-b-a)
  3. 3(a+b-1)
  4. 3(1-b+a)
8

What is the solution of the equation
x log10 (10/3) + log10 3 = log10 (2 + 3x) + x?

  1. 10
  2. 3
  3. 1
  4. 0
9

If x is a real number such that log3 5 = log5 (2 + x), then which of the following is true?

  1. 0 < x < 3
  2. 23 < x < 30
  3. x > 30
  4. 3 < x < 23
10

If n is a whole number greater than 1, then n2(n2 - 1) is always divisible by

  1. 12
  2. 24
  3. 48
  4. 60
11

The sum of two numbers is 10 and their product is 20. What is the sum of their reciprocals?

  1. 1
  2. 1/2
  3. 2
  4. 1/10
12

What is the last digit in 7402 + 3402?

  1. 0
  2. 2
  3. 4
  4. 8
13

The difference between the squares of two consecutive odd integers is always divisible by

  1. 16
  2. 8
  3. 7
  4. 3
14

If x is a positive even integer and y is a negative odd integer, then xy is

  1. even integer
  2. rational number
  3. odd integer
  4. none
15

A student was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was

  1. 15
  2. 32
  3. 12
  4. 25
16

What is the maximum value of m if the number 

N = 35 × 45 × 55 × 60 × 124 × 75 

is divisible by 5m?

  1. 4
  2. 5
  3. 6
  4. 7
17

If n is a natural number, then √n is

  1. always a rational number
  2. always a natural number
  3. always an irrational number
  4. either a natural number or an irrational number
18

The digit in the units place of the product 81×82×83×84×....×99 is

  1. 0
  2. 4
  3. 6
  4. 8
19

If N, N+2 and N+4 are prime numbers, then the number of possible solutions for N are

  1. 1
  2. 2
  3. 3
  4. 4
20

The sum of two numbers is 143. If the greater number is divided by the difference of the numbers, the quotient is 7. What is the difference of the two numbers?

  1. 9
  2. 11
  3. 14
  4. 15
21

The values of x which satisfy the equation 51+x + 51–x = 26 are

  1. –1, 1
  2. 0, 1
  3. 1, 2
  4. –1, 0
22

The number of prime numbers which are less than 100 is

  1. 24
  2. 25
  3. 26
  4. 27
23

What is the remainder when the number (4444)4444 is divided by 9?

  1. 4
  2. 6
  3. 7
  4. 8
24

A car owner buys petrol at Rs. 7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

  1. Rs. 8.50
  2. Rs. 9
  3. Rs. 8
  4. Rs. 7.98
25

A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

  1. Rs. 4991
  2. Rs. 5991
  3. Rs. 6001
  4. Rs. 6991
26

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is

  1. 250
  2. 276
  3. 280
  4. 285
27

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is

  1. 2
  2. 3
  3. 4
  4. 5
28

The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.

  1. 55
  2. 60
  3. 62
  4. 64
29

The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is

  1. 3500
  2. 4000
  3. 4050
  4. 5000
30

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

  1. 22 years
  2. 23 years
  3. 24 years
  4. 25 years
31

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

  1. 6.25
  2. 6.5
  3. 6.75
  4. 7
32

Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

  1. 21 years
  2. 22 years
  3. 23 years
  4. 24 years
33

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is

  1. Rs. 19
  2. Rs. 19.50
  3. Rs. 18
  4. Rs. 18.50
34

The average weight of 10 apples is 0.4 kg. If the heaviest and lightest apples are taken out, the average is 0.41 kg. If the lightest apple weights 0.2 kg, what is the weight of heaviest apple?

35

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

  1. 30
  2. 25
  3. 20
  4. 15
  5. None of the above
36

The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

  1. 30
  2. 28
  3. 32
  4. 26
37

A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to

  1. 5
  2. 20
  3. 30
  4. 35
38

If a quantity is increased by 20% and then decreased by 10%, then what is the net increase or decrease?

  1. 10% Decrease
  2. 10% Increase
  3. 8% Increase
  4. 8% Decrease
39

In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 are not defective. What is the percentage of defective in the stockpile?

  1. 5%
  2. 4%
  3. 3%
  4. 2.5%
40

The pre-paid recharge of Airtel gives 21% less talk time than the same price pre-paid recharge of Vodafone. The post-paid talk time of Airtel is 12% more than its pre-paid recharge, having the same price. Further, the post-paid talk time of same price of Vodafone is 15% less than its pre-paid recharge. How much percent less / more talk time can one get from the Airtel post-paid service compared to the post-paid service of Vodafone?

  1. 3.9% more
  2. 4.7% less
  3. 4.7% more
  4. 2.8% less
41

As a strategy towards retention of customers, the service centre of a split AC machine manufacturer offers discount as per the following rule: for the second service in a year, the customer can avail of a 10% discount; for the third and fourth servicing within a year, the customer can avail of 11% and 12% discounts respectively of the previous amount paid, Finally, if a customer gets more than four services within a year, he has to pay just 55% of the original servicing charges. If Rohan has availed 5 services from the same service centre in a given year, the total percentage discount availed by him is approximately

  1. 16.52
  2. 20.88
  3. 22.33
  4. 24.08
42

Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is

  1. 13600
  2. 13000
  3. 13400
  4. 14000
43

In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to 

  1. 16
  2. 13
  3. 10
  4. 7
44

A fraction, which bears the same ratio to 1/27, that 3/11 does to 5/9, is equal to

  1. 1/11
  2. 3/11
  3. 1/55
  4. 55
45

A, B and C enter into a partnership and their shares are in ratio 1/2 : 1/3 : 1/4, after 2 months, A withdraws half of his capital and after 10 months, a profit of Rs 378 is divided among them. What is B's share?

  1. Rs 124
  2. Rs 144
  3. Rs 156
  4. Rs 165
46

From each of the two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers?

  1. 2 : 3
  2. 3 : 2
  3. 3 : 1
  4. 2 : 1
47

In a certain examination, the number of students who passed, was three times the number of those who were rejected. If there had been 16 fewer candidates and if six more had been rejected, the number of those who passed and of those who were rejected would have been in the ratio 2 : 1. Find the number of candidates?

  1. 120
  2. 130
  3. 136
  4. 156
48

The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is

  1. 20
  2. 30
  3. 48
  4. 58
49

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

  1. 3 : 4
  2. 2 : 3
  3. 1 : 3
  4. 1 : 2
50

A milkman mixes 20 L of water with 80 L of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he has sold. What is the current proportion of water to milk?

  1. 2 : 3
  2. 1 : 2
  3. 1 : 3
  4. 2 : 1