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

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NixonDutt

Intern

Joined: 10 Jun 2018

Posts: 32

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

10 Aug 2018, 15:27

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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

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Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 21032

Re: If p and q are both positive integers such that p/9 + q/10 [#permalink]

11 Aug 2018, 02:08

Expert Reply

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