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# If x and y are positive integers, is xy evenly divisible by

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Joined: 19 Feb 2004
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Location: Lungi
If x and y are positive integers, is xy evenly divisible by [#permalink]

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01 Nov 2004, 04:55
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If x and y are positive integers, is xy evenly divisible by 4?
1. y+2 is divisible by 4.
2. x-2 is divisible by 4.
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4288

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01 Nov 2004, 06:16
C
1) 1 factor of 2 but we know nothing about y
2) 1 factor of 2 but we know nothing about x
both combined, we know that there are 2 factors of 2 in xy
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01 Nov 2004, 10:52
This is my reason:
-->(a) alone does not tell us anything about X,
But it tells us:
y=4k-2
where
k=1,2,3......
-->(b) alone does not tell us anything about Y
But it tells us:
x=4k+2
where
k=1,2,3.....
+++++
Considering both we can see:
(4k-2)(4k+2)=(16k^2 -4)
=4(4k^2-1)

The above term is divisible by 4 as 4 is a factor of the term.Thus the answer is (c).
01 Nov 2004, 10:52
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