TMUA Logic Drill · Necessary Conditions

Medium · Paper 2 Style

Let P be “n is divisible by 12” and Q be “n is divisible by 3”.

Which statement correctly describes Q?

A. Q is sufficient but not necessary for P. B. Q is necessary but not sufficient for P. C. Q is necessary and sufficient for P. D. Q is neither necessary nor sufficient for P.

Correct answer: B

Solution: If n is divisible by 12, then n must be divisible by 3, so Q is necessary. But Q is not sufficient because 6 is divisible by 3 but not by 12.