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OG-12 DS#106

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OG-12 DS#106

by buzzdeepak » Sat Dec 29, 2012 4:15 am
If x and y are integers, is xy even?

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

Why is (1) sufficient?

x could be 3 and y could be 4, xy=15 (Odd)
x could be 2 and y could be 4, xy=10 (Even)
Hence insufficient.

OG explanation says x and y are consecutive, is that a typo in the question?
Please advise, thanks...
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Dec 29, 2012 6:54 am
buzzdeepak wrote:If x and y are integers, is xy even?

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

Why is (1) sufficient?

x could be 3 and y could be 4, xy=15 (Odd)
x could be 2 and y could be 4, xy=10 (Even)
Hence insufficient.

OG explanation says x and y are consecutive, is that a typo in the question?
Please advise, thanks...
There's a problem above (in green).

Statement 1 tells us that x = y+1. In other words, x is 1 greater than y.
So, for example, if y = 2, then x = 2+1 (i.e., x = 3)
Similarly, if y = 9, then x = 10.

Cheers,
Brent
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by Brent@GMATPrepNow » Sat Dec 29, 2012 6:56 am
buzzdeepak wrote:If x and y are integers, is xy even?

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