swerve wrote:If p is a positive integer, and p ≠ 0, is (p^2+p)/(2p) an integer?

(1) p is an even number.
(2) p is a multiple of 3.

The OA is A.

Please, can anyone explain this DS question? I tried to solve it but I can't get the correct answer. I need help. Thanks.

Given: p is a positive integer, and p ≠ 0

To find: Is (p^2+p)/(2p) an integer

(p^2+p)/(2p) can be written as p(p + 1)/(2p) = (p + 1)/2

So, we need to determine whether (p + 1)/2 is an integer.

For (p + 1)/2 to be an integer, (p + 1) must be even or p must be odd.

Question rephrased: Is p odd?

Let's take each statement one by one.

(1) p is an even number.

Sufficient. p is not odd.

(2) p is a multiple of 3.

p: Multiples of 3: {3, 6, 9, 12, ...}

p can be even or odd. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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