If p is an integer, is q an integer?

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If p is an integer, is q an integer? [#permalink]

11 Feb 2012, 18:41

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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.
(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 doesnt tell us if q is an integer, because you dont know anything about r.
Statement (2) is also insufficient: simply knowing that r is an integer isnt 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]

11 Feb 2012, 18:50

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 then Q an integer as well? [#permalink] 11 Feb 2012, 18:50

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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?

If p is an integer, is q an integer?

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