Remainders Divisibility

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

Answer

Since (k+4) is divisible by 7, so remainder when (k+4) is divided by 7 is 0.

k + 2n should be divisible by 7.

k + 2n + 4 - 4 should be divisible by 7.

k + 4 + 2n - 4 should be divisible by 7.

Given that k+4 is already divisible by 7. So, 2n-4 should be divisible by 7.

Out of the 4 options, only n = 9 satisfies this condition.

The correct option is C.