If m is an integer, is m odd?
(1) m/2 is not an even integer.
(2) m - 3 is an even integer
Confused
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- Mike@Magoosh
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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
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
Magoosh GMAT Instructor
https://gmat.magoosh.com/
https://gmat.magoosh.com/
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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
Properties of Quadrilaterals
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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!