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If p is an integer, is q an integer?

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If p is an integer, is q an integer? [#permalink] New post 11 Feb 2012, 17:41
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A
B
C
D
E

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Question Stats:

78% (01:50) correct 22% (00:50) wrong based on 18 sessions
If p is an integer, is q an integer?
(1) The average (arithmetic mean) of p, q, and r is p.
(2) r is an integer.

Ok - this is how I am trying to solve this.
If the average of three numbers is one of the numbers, that means the numbers are equally spaced. p + q + r = 3p
q - p = p - r. In other words, the difference between p and q is equal to the difference between p and r. That doesn’t tell us if q is an integer, because you don’t know anything about r.
Statement (2) is also insufficient: simply knowing that r is an integer isn’t enough to tell you anything about q.
Taken together, the statements are sufficient as integer minus integer will always be an integer.

Is my explanation and thinking correct to arrive at answer C?
[Reveal] Spoiler: OA

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Re: If P is an integer then Q an integer as well? [#permalink] New post 11 Feb 2012, 17:50
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If p is an integer, is q an integer?

(1) The average (arithmetic mean) of p, q, and r is p --> p+q+r=3p --> q+r=2p --> since p is an integer then 2p is an integer --> q+r=integer. Now, if r=integer then q=integer too but if r is not an integer then q also won't be an integer. Not sufficient.

(2) r is an integer. Clearly insufficient.

(1)+(2) From (2) r=integer thus from (1) q=integer. Sufficient.

Answer: C.
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Re: If p is an integer, is q an integer? [#permalink] New post 27 Jun 2015, 15:09
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Re: If p is an integer, is q an integer?   [#permalink] 27 Jun 2015, 15:09
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