Is ab odd? (1) a is even (2) a is an integer

[BTGmoderatorAT]

Is ab odd?

(1) a is even
(2) a is an integer

I can not see how to use statement (1). Experts, could you help me?

[Brent@GMATPrepNow]

Is ab odd?

(1) a is even
(2) a is an integer

Target question: Is ab odd?
Since there's no information stating that b is an integer, we can jump straight to.....

Statements 1 and 2 combined
There are several values of a and b that satisfy BOTH statements. Here are two:
Case a: a = 2 and b = 1, in which case ab = (2)(1) = 2. So, ab is NOT odd
Case b: a = 2 and b = 1.5, in which case ab = (2)(1.5) = 3. So, ab IS odd
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

[Matt@VeritasPrep]

If a is even, then a * b = even * b.

From there, if b is an integer, we must have even * integer = even, but if b is something else (√2, π, ½, whatever) we could have any result we like, be it even, odd, not an integer, not a repeating decimal, etc.

[BTGmoderatorAT]

Is ab odd?

(1) a is even
(2) a is an integer

Target question: Is ab odd?
Since there's no information stating that b is an integer, we can jump straight to.....

Statements 1 and 2 combined
There are several values of a and b that satisfy BOTH statements. Here are two:
Case a: a = 2 and b = 1, in which case ab = (2)(1) = 2. So, ab is NOT odd
Case b: a = 2 and b = 1.5, in which case ab = (2)(1.5) = 3. So, ab IS odd
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

Thanks Brent for showing such a great approach!!!