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# If p, q and r are positive integers and 2p + 3q = r , do r and 6 have

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Math Expert
Joined: 02 Sep 2009
Posts: 56272
If p, q and r are positive integers and 2p + 3q = r , do r and 6 have  [#permalink]

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24 Sep 2018, 06:09
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45% (medium)

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66% (01:35) correct 34% (01:50) wrong based on 42 sessions

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If p, q and r are positive integers and 2p + 3q = r, do r and 6 have a common factor greater than 1?

(1) p is a multiple of 3.
(2) q is a multiple of 3.

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Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: If p, q and r are positive integers and 2p + 3q = r , do r and 6 have  [#permalink]

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24 Sep 2018, 08:06
1
If p, q and r are positive integers and 2p + 3q = r, do r and 6 have a common factor greater than 1?

(1) p is a multiple of 3.
Let p = 3x
$$2p+3q=r...........2*3x+3q=r.........3(2x+q)=r$$
So r is a multiple of 3 and 6 is also multiple of 3, so Ans is YES
Sufficient

(2) q is a multiple of 3.
Let q=3y...
$$2p+3q=r...........2p+3*3y=r$$
Let p be a multiple of 3 then r is a multiple of 3 OR if y=2, r is a multiple of 2 and 6 is also multiple of 2 and 3
In each of the cases above, ans is YES
But say p=2 and y=3 r = 2*2+3*3*3=31, so 31 and 6 do not have common factors other than 1
Insufficient

A
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Re: If p, q and r are positive integers and 2p + 3q = r , do r and 6 have   [#permalink] 24 Sep 2018, 08:06
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