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18 Jul 2018, 02:46
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A
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Difficulty:
35%
(medium)
Question Stats:
65% (01:23) correct
35%
(01:43)
wrong
based on 318
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
M36-54
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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18 Jul 2018, 08:41
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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
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
18 Jul 2018, 09:39
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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
(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
