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Triskaidekaphobia! - m13, Q. 13

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Triskaidekaphobia! - m13, Q. 13 [#permalink] New post 30 Oct 2010, 02:15
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A
B
C
D
E

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Is (x - y)*(x + y) an even integer?

1. x and y are integers
2. [x + y] is even



[Reveal] Spoiler:
Ans = C Query: Whats wrong with B? Only integers can be "even" - so x+y is an Even Integer per Stem 2... can x-y ever be a non integer if x+y is an integer?
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Re: Triskaidekaphobia! - m13, Q. 13 [#permalink] New post 30 Oct 2010, 05:15
The correct answer is C.

(1) - Insufficient. Lets plug in. X=5, Y=2. (5-2)*(5+2)=21, X=4, Y=2, (4+2)*(4-2)=12. Thus BCE.
(2) Insufficient. Let plug in: X=1.3, Y=0.7. (1.3+0.7)*(1.3-0.7)=1.2 (X+Y is even, like is said in the statement). Thus CE

If taken together - Lets plug in X=3 Y=1 , (3+1)*(3-1)=8, X=4 Y=2, (4-2)*(4+2)=12. Sufficient!
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Re: Triskaidekaphobia! - m13, Q. 13 [#permalink] New post 30 Oct 2010, 05:41
Expert's post
gmat1011 wrote:
Is (x - y)*(x + y) an even integer?

1. x and y are integers
2. [x + y] is even



[Reveal] Spoiler:
Ans = C Query: Whats wrong with B? Only integers can be "even" - so x+y is an Even Integer per Stem 2... can x-y ever be a non integer if x+y is an integer?


Answer is C because if x and y are not integers (second statement does not state that), then x+y may be even (statement 2) and (x-y)*(x+y) may not be an integer at all.

Example:
x=1.8 and y=0.2 - answer to the question NO.
x=1.5 and y=0.5 - answer to the question YES.

Statement (1) says that x and y are integers so combined statements guarantee (x-y)*(x+y) being even.

Hope it helps.
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Re: Triskaidekaphobia! - m13, Q. 13   [#permalink] 30 Oct 2010, 05:41
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