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OG 13--DS #111 (Zero an Even Number?)

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OG 13--DS #111 (Zero an Even Number?)

by NDroho » Mon Jun 10, 2013 2:23 pm
If X and Y are integers, is XY even?

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

The simple answer to my question here is: Is 0 an even number? I was under the impression that 0 is just 0--not odd or even.

So with the above said, I found statement 1 not SUFFICIENT with trying any positive number and -1: (-1 * 0 = 0). Statement 2 I found sufficient so I selected B. The correct answer is D, which leads be to believe that 0 is in fact EVEN--is that correct? or is this an error?

Thanks in advance
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by Brent@GMATPrepNow » Mon Jun 10, 2013 2:42 pm
NDroho wrote: If X and Y are integers, is XY even?

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

The simple answer to my question here is: Is 0 an even number? I was under the impression that 0 is just 0--not odd or even.

So with the above said, I found statement 1 not SUFFICIENT with trying any positive number and -1: (-1 * 0 = 0). Statement 2 I found sufficient so I selected B. The correct answer is D, which leads be to believe that 0 is in fact EVEN--is that correct? or is this an error?

Thanks in advance
Zero is an even number. Every integer is either even or odd.
Evens: . . . -6, -4, -2, -0, 2, 4, 6, . . .
Odd: . . . -5, -3, -1, 1, 3, 5, . . .

Here's my full solution.

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
Brent Hanneson - Creator of GMATPrepNow.com
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