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# If p and q are both positive integers such that p/9 + q/10

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Intern
Joined: 10 Jun 2018
Posts: 32
Followers: 0

Kudos [?]: 14 [0], given: 4

If p and q are both positive integers such that p/9 + q/10 [#permalink]  10 Aug 2018, 15:27
00:00

Question Stats:

100% (00:43) correct 0% (00:00) wrong based on 5 sessions
If p and q are both positive integers such that $$\frac{p}{9} + \frac{q}{10}$$ is also an integer, then which one of the following numbers could p equal?

(A) 3
(B) 4
(C) 9
(D) 11
(E) 19

Source : GRE Bible
[Reveal] Spoiler: OA
Moderator
Joined: 18 Apr 2015
Posts: 5202
Followers: 77

Kudos [?]: 1049 [1] , given: 4698

Re: If p and q are both positive integers such that p/9 + q/10 [#permalink]  11 Aug 2018, 02:08
1
KUDOS
Expert's post
Let $$k$$ be an integer such that $$\frac{p}{9} + \frac{q}{10} = k$$.

Since all three numbers $$p$$, $$q$$, and $$k$$ are integers, among the given options, the only case could be:
integer $$(\frac{p}{9})$$ + integer $$(\frac{q}{10})$$ = integer $$(k)$$

C wins
_________________
Re: If p and q are both positive integers such that p/9 + q/10   [#permalink] 11 Aug 2018, 02:08
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