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

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Intern
Joined: 27 Jan 2011
Posts: 3
Is (x-y)*(x+y) an even integer?  [#permalink]

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18 Feb 2011, 06:41
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

44% (01:14) correct 56% (01:29) wrong based on 83 sessions

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

(1) x and y are integers
(2) x+y is even

Could anyone explain why is B not the right answer?

Any number * even = even
so When X+Y is a even number (it doesnt matter what x-y is ?) the entire product will be even.

When statement 2 says x+y may not be an integer at all then how are we assuming that C will be the answer? i.e both the statements are sufficient?
Math Expert
Joined: 02 Sep 2009
Posts: 55228
Re: Is (x-y)*(x+y) an even integer?  [#permalink]

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18 Feb 2011, 07:05
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MRS wrote:
Is (x-y)*(x+y) an even integer?
1. x and y are integers
2. x+y is even

Could anyone explain why is B not the right answer?

Any number * even = even
so When X+Y is a even number (it doesnt matter what x-y is ?) the entire product will be even.

When statement 2 says x+y may not be an integer at all then how are we assuming that C will be the answer? i.e both the statements are sufficient?

The red part is not correct, it should be (any integer)*(even)=(even) (for example 1.3*2=2.6 not an integer at all)

So the 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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Intern
Joined: 27 Jan 2011
Posts: 3
Re: Is (x-y)*(x+y) an even integer?  [#permalink]

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18 Feb 2011, 07:14
Ooops agree typo there about Any integer * even=even

got it thank you for the explanation...
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Joined: 09 Sep 2013
Posts: 10981
Re: Is (x-y)*(x+y) an even integer?  [#permalink]

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13 Mar 2018, 02:20
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Re: Is (x-y)*(x+y) an even integer?   [#permalink] 13 Mar 2018, 02:20
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