Divisibility — CAT Previous-Year Questions

For any natural numbers m, n and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of

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

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

The number of integers x such that 0.25 ≤ 2^x ≤ 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is 

Suppose n is an integer such that the sum of the digits of n is 2, and 10¹⁰ < n < 10¹¹. The number of different values for n is

Let S be the set of integers x such that

(i) 100 < x < 200

(ii) x is odd

(iii) x is divisible by 3 but not by 7

How many elements does S contain?

The integers 34041 and 32506 when divided by a three-digit integer ‘n’ leave the same remainder. What is ‘n’?

The number of positive integer valued pairs (x, y) satisfying 4x – 17y = 1 and x ≤ 1000 is

If m and n are integers divisible by 5, which of the following is not necessarily true?