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Data Suff

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Source: — Data Sufficiency |
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by Frankenstein » Sun Jun 12, 2011 8:14 am
Hi,
(x^2-y^2) = (x+y)(x-y)
From(1): x-y is even.
So, x and y are both odd or both even.
In both cases x+y is even as well. So, (x+y).(x-y) is even*even = multiple of 4
Sufficient

From(2): x+y is even.
So, x and y are both odd or both even.
In both cases x-y is even as well. So, (x+y).(x-y) is even*even = multiple of 4
Sufficient

Hence, D
Cheers!

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by Anurag@Gurome » Sun Jun 12, 2011 8:46 am
vinayreguri wrote:IF x & y are integers , is (x^2-y^2) divisible by 4
i. x-y is even
ii. x+y is even
Statement 1: If (x - y) is even, then either x and y are both even or both odd.
In both the cases, (x + y) is also even.
Hence, (x² - y²) = (x - y)(x + y) = EVEN*EVEN = EVEN

Sufficient

Statement 2: If (x + y) is even, then either x and y are both even or both odd.
In both the cases, (x - y) is also even.
Hence, (x² - y²) = (x - y)(x + y) = EVEN*EVEN = EVEN

Sufficient

The correct answer is D.
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