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# If x is an integer, is y an integer?

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Manager
Joined: 10 Feb 2011
Posts: 112

Kudos [?]: 370 [0], given: 10

If x is an integer, is y an integer? [#permalink]

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15 Mar 2011, 16:46
00:00

Difficulty:

65% (hard)

Question Stats:

37% (00:56) correct 63% (00:47) wrong based on 59 sessions

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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

Last edited by Bunuel on 03 Sep 2017, 06:44, edited 1 time in total.
Edited the OA.

Kudos [?]: 370 [0], given: 10

Manager
Joined: 05 Jan 2011
Posts: 169

Kudos [?]: 195 [0], given: 8

Re: If x is an integer, is y an integer? [#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

Kudos [?]: 195 [0], given: 8

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Re: If x is an integer, is y an integer? [#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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Kudos [?]: 600 [1], given: 40

Manager
Joined: 05 Jan 2011
Posts: 169

Kudos [?]: 195 [0], given: 8

Re: If x is an integer, is y an integer? [#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

Kudos [?]: 195 [0], given: 8

Math Expert
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Posts: 42248

Kudos [?]: 132522 [0], given: 12324

Re: If x is an integer, is y an integer? [#permalink]

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03 Sep 2017, 06:43
banksy wrote:
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.

If x is an integer, is y an integer?

(1) The average (arithmetic mean) of x and y is an integer --> $$\frac{x + y}{2}=integer$$ --> $$x+y=2*integer=integer$$ --> $$y = integer-x=integer-integer=integer$$. Sufficient.

(2) The average (arithmetic mean) of x, y, and y + 4 is x --> $$\frac{x + y+y+4}{3}=x$$ --> $$y=x-2=integer-integer=integer$$. Sufficient.

Answer: D.

Edited the OA, it's D not C.

Similar question to practice from OG: https://gmatclub.com/forum/if-x-is-an-i ... 68098.html
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Kudos [?]: 132522 [0], given: 12324

Re: If x is an integer, is y an integer?   [#permalink] 03 Sep 2017, 06:43
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# If x is an integer, is y an integer?

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