Confused

[soniadiana2011]

If m is an integer, is m odd?
(1) m/2 is not an even integer.
(2) m - 3 is an even integer

[Mike@Magoosh]

Hi, there. I'm happy to help.

Prompt: If m is an integer, is m odd?

Straightforward yes/no prompt.

(1) m/2 is not an even integer.

Well, "not an even integer" is a big category --- that could mean
(a) an odd integer ---> m/2 = 3 ---> m = 6, which is even,
or
(b) not an integer at all ---> m/2 = 5/2 ---> m = 5, which is odd

We can devise scenarios consistent with this statement that give both answers to the prompt question, so this statement, by itself, is insufficient.

(2) m - 3 is an even integer

We know m is an integer. If m - 3 = even, then 3 + (even) = m

We know (odd) + (even) = (odd), so if m = 3 + (even), m must be odd.

Examples: let m - 3 equal even integers
m - 3 = 2 ---> m = 5
m - 3 = 4 ---> m = 7
m - 3 = 6 ---> m = 9
m - 3 = 8 ---> m = 11

By both logic and by numerical plug-in, it's clear that m must be odd. Therefore, statement #2 is sufficient.

Answer = B

Here's a blog you may find helpful.
https://magoosh.com/gmat/2012/integer-pr ... ion-topic/

Does all this make sense? Let me know if you have any further questions.

Mike

[amit28it]

The solution provided by Mike@Magoosh is the most simple and the method used by him is also not very difficult and my answer for the question is same that is B.
Properties of Quadrilaterals

[soniadiana2011]

Thank you once again. I had problem understanding the part " not an even integer". So I thought it to be a straight ODD. That was my mistake!