CAT Number Systems Questions & Solutions

A sample of real CAT Number Systems past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 137 Number Systems questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is

   Answer: 6

2. Q2.CAT 2024

   The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64.Then, the largest number in the original set of three numbers is

   Answer: 70

3. Q3.CAT 2022

   For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is

   • 4

   • 7

   • 6

   • 5

4. Q4.CAT 2020

   How many pairs(a, b) of positive integers are there such that $a\leq b$ and $ab=4^{2017}$ ?

   • 2018

   • 2019

   • 2017

   • 2020

5. Q5.CAT 2017

   If $a, b, c,$ and $d$ are integers such that $a+b+c+d=30$ then the minimum possible value of $(a - b)^{2} + (a - c)^{2} + (a - d)^{2}$ is
   

   Answer: 2

6. Q6.CAT 2005

   If R = $(30^{65}-29^{65})/(30^{64}+29^{64})$ ,then

   • $0<R\leq0.1$

   • $0.1<R\leq0.5$

   • $0.5<R\leq1.0$

   • $R>1.0$

7. Q7.CAT 2003

   A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

   • 31

   • 63

   • 75

   • 91

8. Q8.CAT 2001

   Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

   • $y(x-z)^2$ is even

   • $y^2(x-z)$ is odd

   • $y(x-z)$ is odd

   • $z(x-y)^2$ is even

9. Q9.CAT 2000

   Let S be the set of integers x such that:

   1) 100 <= x <= 200

   2) x is odd

   3) x is divisible by 3 but not by 7.

   How many elements does S contain?

   • 16

   • 12

   • 11

   • 13

10. Q10.CAT 1999

    If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is/are true?

    A. n is odd

    B. n is prime

    C. n is a perfect square

    • A and C only

    • A and B only

    • A only

    • None of these

11. Q11.CAT 1997

    If n is an integer, how many values of n will give an integral value of $\frac{(16n^2+ 7n+6)}{n}$ ?

    • 2

    • 3

    • 4

    • None of these

12. Q12.CAT 1991

    What is the greatest power of 5 which can divide 80! exactly?

    • 16

    • 20

    • 19

    • None of these

CAT Number Systems previous year questions with solutions — AthenaPrep