Inequalities Questions for the CAT exam are part of the Quant section in the CAT exam. Through Inequalities questions, aspirants are tested on concepts related to Modulus functions and the range of inequalities. The difficulty level of the Inequalities questions can be easy to moderate.

**CAT Inequalities Practice questions for the CAT exam**

**Q 1. **How many positive integer values can x take that satisfy the inequality (x - 8) (x - 10) (x - 12).......(x - 100) < 0?

A. 25

B. 30

C. 35

D. 40

**Answer:** B

**Q 2.** Find the range of x for which (x + 2) (x + 5) > 40?

**Answer**: x < -10 or x > 3

**Q 3.** Let n and m be two positive integers such that there are exactly 41 integers greater than 8 m and less than 8 n, which can be expressed as powers of 2. Then, the smallest possible value of n m+ is

A. 44

B. 16

C. 42

D. 14

**Answer**: C

**Q 4. **The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is

**Answer:** 468

**Q 5. **Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

A. 16

B. 21

C. 17

D. 20

**Answer**: B

**Must-do Inequalities questions for the CAT exam**

**Q 6.** There are three persons A B,and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2 kg x . If the weight of E is 12 kg more than that of D , then the value of x is

A. 1.5

B. 0.5

C. 1

D. 2

**Answer: **C

**Q 7. **Three numbers A, B and C are such that the difference between the highest and the second highest two-digit numbers formed by using two of A, B and C is 5. Also, the smallest two two-digit numbers differ by 2. If B > A > C then what is the value of B?

A. 1

B. 6

C. 7

D. 8

**Answer:** B

**Q 8**. The difference between the number of numbers from 2 to 100 which are not divisible by any other number except 1 and itself and the numbers which are divisible by at least one more number along with 1 and itself.

A. 25

B. 50

C. 49

D. can’t be determine

**Answer:** C

**Q 9.** The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7 , and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is

**Answer**: D

**Most Important Inequalities Question for CAT**

**Q 10.** When the difference between the number 842 and its reverse is divided by 99, the remainder will be

A. 0

B. 1

C. 74

D. 17

**Answer:** A

**Q 11:** When the difference between the number 783 and its reverse is divided by 99, the quotient will be

A. 1

B. 10

C. 3

D. 4

**Answer**: D

**Q 12:** Find the number of numbers from 1 to 100 which are not divisible by 2.

A. 51

B. 50

C. 49

D. 48

**Answer: **B

**Q 13:** Find the number of numbers from 1 to 100 that are not divisible by any one of 2, 3, and 5.

A. 26

B. 27

C. 29

D. 32

**Answer:** A

**Q 14.** The last digit of the number obtained by multiplying the numbers 81 × 82 × 83 × 84 × 85 × 86 × 87 × 88 × 89 will be

A. 0

B. 9

C. 7

D. 2

**Answer**: A

**Find Some Previous Year Inequalities Questions for CAT**

**Q 15.** The sum of the digits of a two-digit number is 10, while when the digits are reversed, the number decreases by 54. Find the changed number.

A. 28

B. 19

C. 37

D. 46

**Answer**: D

**Q 16**. When we multiply a certain two-digit number by the sum of its digits, 405 is achieved. If you multiply the number written in reverse order of the same digits by the sum of the digits, we get 486. Find the number.

A. 81

B. 45

C. 36

D. 54

**Answer:** B

**Q 17.** The sum of two numbers is 15 and their geometric mean is 20% lower than their arithmetic mean. Find the numbers.

A. 11, 4

B. 12, 3

C. 13, 2

D. 10, 5

**Answer**: A

**Q 18**. The difference between two numbers is 48 and the difference between the arithmetic mean and the geometric mean is two more than half of 1/3 of 96. Find the numbers.

A. 49, 1

B. 12, 60

C. 50, 2

D. 36, 84

**Answer: **A

**Q 19.** In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

**Answer:** 54

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