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# If both m and n are positive integers, is m a multiple of n?

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Math Expert
Joined: 02 Sep 2009
Posts: 50621
If both m and n are positive integers, is m a multiple of n?  [#permalink]

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18 Jul 2018, 01:46
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Question Stats:

50% (00:58) correct 50% (01:23) wrong based on 33 sessions

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GMAT CLUB TESTS' FRESH QUESTION

If both m and n are positive integers, is m a multiple of n?

(1) m + 3n is a multiple of n
(2) 2m + n is a multiple of n

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If both m and n are positive integers, is m a multiple of n?  [#permalink]

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18 Jul 2018, 07:41
To find whether m is a multiple of n ?

Statement 1

m + 3n is a multiple of n

=> (m + 3n) = n * C (C is some integer)

=> m = nC - 3n

=> m = n(C - 3n)

m is a multiple of n

Statement 1 is sufficient

Statement 2

2m + n is a multiple of n

=> 2m + n = n * C (C is some integer)

=> 2m = n * C - n

=> 2m = n(C - 1)

=> m = $$\frac{n(C-1)}{2}$$

We don't know the divisibility of either "n" or "C-1" with respect to "2"

Hence we can't say m is a multiple of n

Statement 2 is insufficient

Hence option A
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Re: If both m and n are positive integers, is m a multiple of n?  [#permalink]

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18 Jul 2018, 08:39
If both m and n are positive integers, is m a multiple of n?

(1) m + 3n is a multiple of n
m+3n is a multiple of n...
3n is a multiple of n, so m has to be a multiple of n otherwise 3n+m will not be a multiple of n
Sufficient

(2) 2m + n is a multiple of n
2m+n is a multiple of n..
Now n is a multiple of n so 2m will be a multiple of n..
but we cannot say if m is a multiple of n...
Say m is 12 and y is 4.....2m or 24 and also m or 12 is multiple of n or 4
But say m is 6 and y is 4.....2m or 12 is a multiple of n or 4, but m or 6 is not a multiple of 4
Insufficient

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If both m and n are positive integers, is m a multiple of n? &nbs [#permalink] 18 Jul 2018, 08:39
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