Doubt - If m is an integer, is m odd?

jaspreetsra wrote:If m is an integer, is m odd?
(1) m/2 is not an even integer.
(2) m-3 is an even integer.
Source: The official guide for GMAT 13 edition
(1) m = 2, 6, 10, and so on - fulfills the condition. So, m is even i.e. definite answer - no. Sufficient
(2) m = 5, 7, and so on, so m is odd i.e. definite answer –yes. Sufficient.
My answer is D.
Should it be B? WHy?

You are assuming that m/2 must be an integer.
m = 1, 3, 5 etc ALSO fulfills the condition that m/2 is not an even integer
Do, m can be EITHER even OR odd.

Cheers,
Brent

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

Target question: Is m odd?

Statement 1: m/2 is not an even integer.
There are several values of m that satisfy this condition. Here are two:
case a) m = 3 (3/2 is not an even integer), which means m is ODD
case b) m = 6 (6/2 is not an even integer), which means m is EVEN
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: m - 3 = an EVEN integer
Rewrite as m = EVEN + 3
3 is ODD, so we get: m = EVEN + ODD
Simplify: m = ODD [since EVEN + ODD = ODD]
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

jaspreetsra wrote:If m is an integer, is m odd?
(1) m/2 is not an even integer.
(2) m-3 is an even integer.
Source: The official guide for GMAT 13 edition
(1) m = 2, 6, 10, and so on - fulfills the condition. So, m is even i.e. definite answer - no. Sufficient
(2) m = 5, 7, and so on, so m is odd i.e. definite answer –yes. Sufficient.

We are given that m is an integer, and we must determine whether it is odd.

Statement One Alone:

m/2 is not an even integer.

The information in statement one is not enough to determine whether m is odd since m can be odd or even. For example, if m = 3 (an odd number), m/2 = 3/2 = 1.5 is not an even integer. On the other hand, if m = 2 (an even number), m/2 = 2/2 = 1 is also not an even integer.

Thus, statement one is not sufficient to determine whether m is odd.

Statement Two Alone:

m – 3 is an even integer.

Since m – 3 is an even integer, we can say m – 3 = even. That is, m = even + 3. Since 3 is odd and we know that even + odd = odd, we know that m must be an odd integer.

Statement two is sufficient to answer the question.

Answer: B