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

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Manager
Joined: 10 Feb 2011
Posts: 114
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Kudos [?]: 222 [0], given: 10

(MH) If x is an integer, is y an integer? (1) The average [#permalink]

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15 Mar 2011, 16:46
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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
Joined: 05 Jan 2011
Posts: 178
Followers: 5

Kudos [?]: 106 [0], given: 8

Re: 8. (MH) If x is an integer, is y an integer? (1) The averag [#permalink]

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15 Mar 2011, 19:16
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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Location: United States (IN)
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Kudos [?]: 491 [1] , given: 36

Re: 8. (MH) If x is an integer, is y an integer? (1) The averag [#permalink]

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15 Mar 2011, 19:36
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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
Joined: 05 Jan 2011
Posts: 178
Followers: 5

Kudos [?]: 106 [0], given: 8

Re: 8. (MH) If x is an integer, is y an integer? (1) The averag [#permalink]

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15 Mar 2011, 20:34
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, 20:34
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(MH) If x is an integer, is y an integer? (1) The average

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