Question

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

• A. $m - n$ is divisible by 5
• B. $m^2 - n^2$ is divisible by 25
• C. $m + n$ is divisible by 10
• D. None of these

Hint:

Always check divisibility conditions carefully — extra factors require additional conditions.

Answer 1

The Correct Option is C

If $m = 5a, n = 5b$: (a) $m - n = 5(a - b)$ → divisible by 5 (true). (b) $m^2 - n^2 = 25(a^2 - b^2)$ → divisible by 25 (true). (c) $m + n = 5(a + b)$ → divisible by 5, not necessarily 10 unless $a + b$ is even (not guaranteed).