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(MH) If x is an integer, is y an integer? (1) The average

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Manager
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(MH) If x is an integer, is y an integer? (1) The average [#permalink] New post 15 Mar 2011, 15:46
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A
B
C
D
E

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8. (MH) If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.
[Reveal] Spoiler: OA
Manager
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Re: 8. (MH) If x is an integer, is y an integer? (1) The averag [#permalink] New post 15 Mar 2011, 18:16
banksy wrote:
8. (MH) If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.



1. (x + y)/2 is an integer
i.e x + y => integer
Therefore Y is an integer since x is an integer and X+Y is also an integer
eg . x+y=5 IF x=3 then y will be 2 (both integer)
Similarly if x=2.5 y will be 2.5 (both non integer) sufficient

2. x+y+y+4=3x
x-y=4
x is an integer (x-y) is an integer .... therefore y must also be an integer sufficient
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Re: 8. (MH) If x is an integer, is y an integer? (1) The averag [#permalink] New post 15 Mar 2011, 18:36
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I think the OA is wrong, it should be D.

From (1), (x+y)/2 = k, where k is an integer, so y = 2k - x, an integer - integer = integer, so (1) is sufficient.

From (2) (x + y + y + 4)/3 = x => x + 2y + 4 = 3x => 2x-2y = 4 => x-y = 2, so y = x + 2, an integer + integer = integer, so (2) is sufficient.

Hence the answer is D.
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Manager
Manager
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Joined: 05 Jan 2011
Posts: 178
Followers: 3

Kudos [?]: 21 [0], given: 8

GMAT Tests User
Re: 8. (MH) If x is an integer, is y an integer? (1) The averag [#permalink] New post 15 Mar 2011, 19:34
banksy wrote:
8. (MH) If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x and y is an integer.
(2) The average (arithmetic mean) of x, y, and y + 4 is x.



hey,
Please share with us the souce.... OA seems to be wrong
Re: 8. (MH) If x is an integer, is y an integer? (1) The averag   [#permalink] 15 Mar 2011, 19:34
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(MH) If x is an integer, is y an integer? (1) The average

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