number system

nikhilagrawal wrote:If a, b, and c are integers, and the product abc is even, is b even?

Let's start with step 1 of the Kaplan method for DS: dissect the question stem.

If abc is even, then at least one of the 3 integers must be even. (i.e. we could have all even, 2 evens and 1 odd or 1 even and 2 odds.)

Step 2: look at each statement by itself.

(1) (ab)/c is an even integer.

For ab/c to be even, we could have even/odd (e.g. 12/3) or even/even (e.g. 12/6). So, we know that ab must be even, which means that at least one of a or b must be even.

Accordingly, b could be even or odd: insufficient.

(2) (ac)/b is an odd integer.

For ac/b to be odd, we could have even/even (e.g. 12/4) or odd/odd (e.g. 15/3).

However, the only way to get odd/odd would be for all 3 of a, b and c to be odd, which we know is impossible based on the question stem (since abc is even).

Therefore, we know that b MUST be an even integer: sufficient.

(2) is sufficient but (1) isn't: choose (B).

thanks .. u gave a very simple soln.. I was playing with nos and got confused ....

gr8 expln...