Number properties - Even & Odd ( pls help )

[sweet.prakash1]

Data comparison Question: The product of integers f,g and h is even and the product of integers f and g is odd.

quantity A -The remainder when f is divided by 2.
quantity B -The remainder when h is divided by 2.

Answer specified: A

Doubt: since question specifies only integers? Why can't I consider the integers to be -ve??

i.e., from the question it is evident that, h is a even number. ( can be positive or negative )

If only positive integer is considered, answer A is correct. If we consider negative integer also, answer seems to be wrong. Can some one help me with this?

[tommywallach]

Hey Prakash,

I'm not sure how it makes a different. Here's an assignment for you. If you want to prove that the answer is (D) here, please provide actual numbers for f, g, and h that prove both situations (where one column is bigger and where the other column is bigger). To do well on the GRE, it isn't enough just to think about what might make things happen. You need to consider actual numbers.

-t

[sweet.prakash1]

Hey Tommywallach,

Thanks for your time. I have explained my logic below.
"
The product of integers f,g and h is even and the product of integers f and g is odd.
quantity A -The remainder when f is divided by 2.
quantity B -The remainder when h is divided by 2.

Answer specified: A"

From the question it is evident that h is a even number where as f and g are odd numbers.

First case consider: h to positive even number and f to be positive odd number.
f = 3 ( 3/2 remainder is 1 ) h = 2 ( 2/2 remainder = 0 )
so answer is A perfect!!!

Second case consider: h to positive even number and f to be negative odd number itself.
f = -3 ( -3/2 remainder = -1 ) h = 2 ( 2/2 remainder = 0 )
In this case answer is B.

so final answer should be D.

What am i missing here can you please correct my mistake ?

[tommywallach]

Hey Sweet,

I see the problem. The GRE doesn't test negative remainders. Is that one of OUR questions? If so, we need to change it to clarify that everything is positive. Negative remainders exist in real math, but not on the GRE. Real questions will always make clear that the remainder can't be negative (because the original integers will be positive).

-t