number system

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nikhilagrawal: Senior | Next Rank: 100 Posts; Posts: 81; Joined: Thu Jun 12, 2008 1:57 pm; Thanked: 1 times

number system

by nikhilagrawal » Wed Sep 17, 2008 11:07 am

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

(1) (ab)/c is an even integer.
(2) (ac)/b is an odd integer.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question

I dont have any OA

Quote

Source: Beat The GMAT — Data Sufficiency | Wed Sep 17, 2008 11:07 am

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: number system

by Stuart@KaplanGMAT » Wed Sep 17, 2008 11:19 am

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).