If m is an integer, is m odd?

(1) m/2 is not an even integer.
(2) m – 3 is an even integer.

can some body please explain to me why A is INSUFFICIENT

i see it this way

given that select those items which make m/2 <> even

so take
m = 6, 10, -10, -14 etc

they give 3,5,-5,-7 etc...

so m is even , so is m odd is answered in NEGATIVE.....so this is sufficient to answer the question right?

can some please explain why it is INSUFFICIENT
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Harsha

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Isn't \frac{m}{2} said to be an integer (though not even)? So that \frac{5}{2} is not the case.

Posted from GMAT ToolKit

(1) m/2 is not an even integer

(2) m-3 is an even integer


I was a bit confused about what statement 1 even meant to be honest. The correct answer is B (only state 2 being sufficient). Can someone help me understand what statement 1 is saying... as well as why it is insufficient? Thanks!

For fact statement 1, take (m/2)=3,7,5 etc .. you get all values of "m" as even. So your ans to the problem statement is a NO. Now take, m/2=1.5 Thus here we see that m=odd, hence a Yes. So statement A is not sufficient.

Hi ahatoval, this is a common mistake the GMAT likes to exploit, so it's good to have a complete understanding of it. The key is keeping track of what must be an integer, and what doesn't have to be.

Statement 2 is correct because m has to be an integer, so any odd integer -3 (or -5 or -7) would be even. Sufficient.

You seem to be more concerned with statement 1. This statement tells us that m is an integer, but that m/2 is not an even integer. This is not the same thing as being an odd integer. Let's look at values of m/2 for different m's

m=1 --) m/2 = 0.5
m=2 --) m/2 = 1
m=3 --) m/2 = 1.5
m=4 --) m/2 = 2
...
pattern repeats

Therefore, if m/2 is not an even integer, then m=4 is excluded from the list of possibilities. This leaves m=1, m=2 and m=3. M/2 can therefore be an odd integer or a non-integer. Since we have examples of both, we cannot conclude with certainty whether m is an odd integer, it can be either 1 or 2 or 3 (or 5 or 6 or 7...)

The assumption you make that leads you down the rabbit hole on this question is that m/2 must be an integer. This is not stated in the question and easily demonstrated to be false with a few small examples. On Data Sufficiency, it's often a good idea to try a few numbers and see if you can discern a pattern.

Hope this helps!
-Ron
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Ron Awad
Veritas Prep | GMAT Instructor
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Thanks, Ron . Totally makes sense.

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