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smushkas: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Jul 01, 2007 5:56 pm; Thanked: 3 times

by smushkas » Tue Mar 04, 2008 7:12 pm

Hey there,

Can anyone explain this problem? I have the explanation, but I can't quite catch the logic behind the question.

Both x and y are integers. In all cases where x is even, y is also even. Is xy even?

[1] y - x is odd

[2] sqrt[xy] = 6

Thanks in advance!

OA [spoiler] D [/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Tue Mar 04, 2008 7:12 pm

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

Re: Kaplan DS

by Stuart@KaplanGMAT » Tue Mar 04, 2008 8:13 pm

smushkas wrote:Hey there,

Can anyone explain this problem? I have the explanation, but I can't quite catch the logic behind the question.

Both x and y are integers. In all cases where x is even, y is also even. Is xy even?

[1] y - x is odd

[2] sqrt[xy] = 6

Thanks in advance!

OA [spoiler] D [/spoiler]

Is xy even?

Since x and y are integers, xy will be even if x OR y is even. So, the question is really asking:

is either x or y even?

(1) y - x is odd. Well, the only way to get an odd difference is an even - an odd or an odd - an even. Therefore, y is even and x is odd (since if x was even, y would have to be as well). Y is even, therefore xy is even: sufficient.

(2) sqrt(xy) = 6

If we square both sides, we get xy = 36, which is even: sufficient.

Each of (1) and (2) are sufficient alone: choose (d).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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xilef: Master | Next Rank: 500 Posts; Posts: 111; Joined: Thu Jan 31, 2008 4:05 pmFollowed by: 1 member; Thanked: 18 times

by xilef » Wed Mar 05, 2008 12:01 pm

What's the purpose of this statement in the question : 'In all cases where x is even, y is also even' - doesn't it suggest that xy is even*even?

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

by Stuart@KaplanGMAT » Wed Mar 05, 2008 1:26 pm

xilef wrote:What's the purpose of this statement in the question : 'In all cases where x is even, y is also even' - doesn't it suggest that xy is even*even?

It's a one-way conditional statement:

"if x is even, then y is even".

So, there are 3 possibilities:

x even, y even
x odd, y even
x odd, y odd

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