even/odd integer

[mtripathy]

Source: OG 13th

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

OA:B

I doubt the OA as St.1 is also sufficient. St 1 says m/2 is odd. Any integer "m" divided by 2 will become odd only when m is even. No odd value of m divided by 2 will result an integer. Hence it gives a clear answer that m is even and sufficient for the yes/no question.

Can any expert please clarify?

[GMATGuruNY]

Source: OG 13th

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

OA:B

I doubt the OA as St.1 is also sufficient. St 1 says m/2 is odd. Any integer "m" divided by 2 will become odd only when m is even. No odd value of m divided by 2 will result an integer. Hence it gives a clear answer that m is even and sufficient for the yes/no question.

Can any expert please clarify?

Statement 1: m/2 is not an even integer.
It's possible that m=1, since 1/2 is not an even integer.
In this case, m is odd.
It's possible that m=2, since 2/2=1 is not an even integer.
In this case, m is even.
INSUFFICIENT.

Statement 2: m-3 is an even integer.
m - 3 = even.
Thus:
m = even + 3 = even + odd = odd.
SUFFICIENT.

The correct answer is B.

[mtripathy]

Statement 1: m/2 is not an even integer.
It's possible that m=1, since 1/2 is not an even integer.
In this case, m is odd.
It's possible that m=2, since 2/2=1 is not an even integer.
In this case, m is even.
INSUFFICIENT.

If m=1, then 1/2 is neither an odd nor an even integer because 1/2 is not an integer. m/2 will result an integer only m is an even integer. Hence m is always an even integer in this case and the answer is no for the y/n question. Am I thinking in the right way?

[mtripathy]

Statement 1: m/2 is not an even integer.
It's possible that m=1, since 1/2 is not an even integer.
In this case, m is odd.
It's possible that m=2, since 2/2=1 is not an even integer.
In this case, m is even.
INSUFFICIENT.

Dear Mitch,
If m=1, then 1/2 is neither an odd nor an even integer because 1/2 is not an integer. m/2 will result an integer only m is an even integer. Hence m is always an even integer in this case and the answer is no for the y/n question. Am I thinking in the right way?

[anuprajan5]

Hi,

Statement 1 says that m/2 is not an even integer.

If you have m as 1 or 2 (odd and even respectively), you end up with m/2 which is not an even integer. Only for cases where m was greater than 2 could you conclusively use the logic that m would definitely be an odd number because then you would have only 2 options:

a. An odd number divided by 2 would not be an even integer.
b. An even number greater than 2 would always be an even integer.

Regards
Anup

[GMATGuruNY]

Statement 1: m/2 is not an even integer.
It's possible that m=1, since 1/2 is not an even integer.
In this case, m is odd.
It's possible that m=2, since 2/2=1 is not an even integer.
In this case, m is even.
INSUFFICIENT.

If m=1, then 1/2 is neither an odd nor an even integer because 1/2 is not an integer. m/2 will result in an integer only if m is an even integer. Hence m is always an even integer in this case and the answer is no for the y/n question. Am I thinking in the right way?

The portion in red overly restricts statement 1, which does NOT require that m/2 yield an integer.
Quite the opposite: statement 1 indicates that m/2 is NOT an even integer.
Since m=1 yields m/2 = 1/2 -- which is not an even integer -- m=1 satisfies statement 1.
In this case, the answer to the question stem is YES, since m=1 is ODD.
It should be noted that ANY ODD INTEGER will satisfy statement 1:
If m=3, then m/2 = 3/2.
If m=5, then m/2 = 5/2.
If m=101, them m/2 = 101/2.
In each case, m/2 is not an even integer.