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OG12 #106: if x and y are integers, is xy even?

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by Fractal » Wed Sep 15, 2010 6:46 am
if x and y are integers, is xy even?

(1) x = y + 1
(2) x/y is an even integer

according to og, the solution is: D

Why is (1) sufficient? I mean, x could be 1 and y could be 0 --> xy would not be even, because xy = 0! but x could also be 2 and y=1, then xy=2 which is even! so for me, (1) is insufficient!

?

thx for hlp
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by beatthegmatinsept » Wed Sep 15, 2010 7:43 am
Fractal wrote:if x and y are integers, is xy even?

(1) x = y + 1
(2) x/y is an even integer

according to og, the solution is: D

Why is (1) sufficient? I mean, x could be 1 and y could be 0 --> xy would not be even, because xy = 0! but x could also be 2 and y=1, then xy=2 which is even! so for me, (1) is insufficient!

?

thx for hlp
Your logic on (a) is correct, except that in the only scenario where you get 0 as xy, that qualifies as an even integer as well. 0 is never considered odd, its considered even. I just googled it to confirm :)
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by selango » Wed Sep 15, 2010 7:52 am
Fractal wrote:if x and y are integers, is xy even?

(1) x = y + 1
(2) x/y is an even integer

according to og, the solution is: D

Why is (1) sufficient? I mean, x could be 1 and y could be 0 --> xy would not be even, because xy = 0! but x could also be 2 and y=1, then xy=2 which is even! so for me, (1) is insufficient!

?

thx for hlp
Check the properties for integer Zero in OG.

0 is even integer.

0 is neither positive nor odd.
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by Fractal » Wed Sep 15, 2010 7:53 am
thx a lot

and i am sorry for that question. i should have known it! i just looked it up in kaplan; 0 is even!
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by buzzdeepak » Sat Dec 29, 2012 4:06 am
What if x=2 and y=4?

OG solution says they are consecutive but the question doesn't state that....

IMO Ans= B.
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by Brent@GMATPrepNow » Sat Dec 29, 2012 6:58 am
Fractal wrote:if x and y are integers, is xy even?

(1) x = y + 1
(2) x/y is an even integer
When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

Target question: Is xy even?

Aside: For xy to be even, we need x to be even, or y to be even (or both even).

Statement 1: x = y+1
This tells us that x is 1 greater than y.
This means that x and y are consecutive integers.
If x and y are consecutive integers, then one must be odd and the other must be even.
As such, the product xy must be even.
So, statement 1 is SUFFICIENT

Statement 2: x/y is an even integer.
If x/y is an even integer, then we can write x/y = 2k (where k is an integer)
Now take the equation and multiply both sides by y to get: x = 2ky
If k and y are both integers, we can see that 2ky (also known as x) must be even.
If x is even, then the product xy must be even.
So, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
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by kaiweiweiwei » Sun Dec 30, 2012 5:54 pm
If y=0 and x=1, is xy still even?

I forget if 0 is even or not.
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by Brent@GMATPrepNow » Sun Dec 30, 2012 5:58 pm
0 is, indeed, even.

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Brent
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