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Sharpen Your Basics with CAT Number System Practice Questions with Solutions

1. CAT - Number System

When 1313 is divided by a positive integer x, the remainder is 17. How many values of x are possible?

Correct Answer

16
Video Explanation

2. CAT - Number System

N is a number having exactly 4 factors and is not a perfect cube. Sum of all it’s factors excluding the number itself is 2014. Find N.

Correct Answer

4022
Video Explanation

3. CAT - Number System

Using all the digits 0,1,2,3,4,5,6 exactly once, Find the greatest number divisible by 55

Correct Answer

6431205
Video Explanation

4. CAT - Number System

If a,b,c and d are integers, where a+b+c+d=4 then find the minimum value of 1/a+1/b+1/c+1/d.

Correct Answer

-20/7
Video Explanation

5. CAT - Number System

If N = 364 x n5 , where N is a positive integer, has 182 factors, how many possible values N can assume?

Correct Answer

2 Possibilities
Video Explanation

6. CAT - Number System

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

Correct Answer

70
Video Explanation

7. CAT - Number System

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4- digit number satisfying the above conditions is: 

Correct Answer

4195
Video Explanation

8. CAT - Number System

For all possible integers n satisfying 2.25 ≤ 2 + 2n+2 ≤ 202, the number of integer values of 3 + 3n+1 is:

Correct Answer

7
Video Explanation

9. CAT - Number System

If n is a positive integer such that (7√10) (7√10)2…… (7√10)n  is greater than 999, then the smallest value of n is

Correct Answer

6
Video Explanation

10. CAT - Number System

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

Correct Answer

6
Video Explanation

11. CAT - Number System

If a, b, c are non-zero and 14a = 36b = 84c, then 6b(1/c – 1/a) is equal to:

Correct Answer

3
Video Explanation

12. CAT - Number System

Let m and n be natural numbers such that n is even and 0, 2 less than m/20, n/m, n/11 less than 0.5.

Then m – 2n equals:

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

Correct Answer

4. 1
Video Explanation

13. CAT - Number System

How many of the integers 1, 2, ….., 120, are divisible by none of 2, 5 and 7?
  1. 40
  2. 42
  3. 41
  4. 43

Correct Answer

3. 41
Video Explanation

14. CAT - Number System

2521 – 921 is not divisible by which one of the following :
  1. 16
  2. 98
  3. 544
  4. 14896

Correct Answer

3. 544
Video Explanation

15. CAT - Number System

ABCD is a 4 digit number having all distinct digits such that AB is a 2 digit prime number, CD is also a 2 digit -prime number and BC is a 2 digit perfect square. How many such numbers are possible?

Correct Answer

12
Video Explanation

16. CAT - Number System

Let X be a four-digit number with exactly three consecutive digits being the same and is a multiple of 9. How many such values of X are possible?

Correct Answer

20
Video Explanation

Understanding Number System

The Number System section of the Quantitative Aptitude paper for the CAT exam tests candidates on such basic concepts as factors, factorials, HCF and LCM, base systems, and remainders. In the CAT 2025 exam, about 2-3 questions are likely to fall in this category. The best way to understand these concepts would be take help of free CAT questions at Quantifiers that have solutions as well as video explanations. The Number System is an essential part of the CAT quantitative section, and mastering it requires familiarity with several tricks, shortcuts, and formulas that help in solving problems in a much faster way. Such techniques are explained in great detail by CAT experts through the video solutions provided.
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