Divisibility

1

56 - 1 is divisible by

  1. 5
  2. 13
  3. 31
  4. None of these
2

If n is any odd number greater than 1, then n(n2 - 1) is

  1. divisible by 24 always
  2. divisible by 96 always
  3. divisible by 48 always
  4. None of these
3

Let N = 553 + 173 - 723. N is divisible by

  1. both 3 and 17
  2. both 7 and 13
  3. both 3 and 13
  4. both 17 and 7
4

What will be remainder when (6767 + 67) is divided by 68?

  1. 67
  2. 63
  3. 66
  4. 1
5

Find the minimum integral value of n such that the division 55n/124 leaves no remainder

  1. 124
  2. 123
  3. 31
  4. 62
6

Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals

  1. 7
  2. 5
  3. 9
  4. 3
7

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p2 - 1) is

  1. always divisible by 6, and may or may not be divisible by 12
  2. always divisible by 24
  3. never divisible by 6
  4. always divisible by 12, and may or may not be divisible by 24