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m and n

by GmatKiss » Thu May 10, 2012 3:11 am
If m and n are nonzero integers, is m/n an integer?

(1) 2m is divisible by n

(2) m is divisible by 2n
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Source: — Data Sufficiency |
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by niketdoshi123 » Thu May 10, 2012 4:20 am
GmatKiss wrote:If m and n are nonzero integers, is m/n an integer?

(1) 2m is divisible by n

(2) m is divisible by 2n
By plugging in numbers

statement 1

case 1
m=3 (odd)
n=2 (even)
2m=6

Here 2m is divisible by n
but m/n is not an integer NO

case 2
m=4 (even)
n=2 (even)
2m=8

here 2m is divisible by n
and m/n is an integerYES

Hence INSUFFICIENT

Statement 2
case 1
m=18 (even)
n=3 (odd)
2n=6

Here m is divisible by 2n 18/6=3
and m/n is an integer 18/3= 6 YES

case 2
m=16 (even)
n=4 (even)
2n=8

Here m is divisible by 2n
and m/n is also an integer 16/4=4 YES

Hence Sufficient
the answer is B
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by Brent@GMATPrepNow » Thu May 10, 2012 6:16 am
GmatKiss wrote:If m and n are nonzero integers, is m/n an integer?
(1) 2m is divisible by n
(2) m is divisible by 2n
Let's rephrase this target question.
If m/n is an integer, then we know that m = nk where k is an integer.
So, let's rephrase this target question as: Does m = kn for some integer k?

Statement 1: 2m is divisible by n
This means that 2m = qn for some integer q.
Divide both sides by 2 to get: m = (q/2)n
Do we have enough information to answer the target question? In other words, Does m = kn for some integer k?
Since (q/2) may or may not be an integer, we do not have sufficient information.

Statement 2: m is divisible by 2n
This means that m = q(2n) for some integer q.
Or we can write: m = 2qn
Do we have enough information to answer the target question? In other words, Does m = kn for some integer k?
Yes! Since q is an integer, we know that (2q) must be an integer.
So, we can be certain that m = kn for some integer k?
As such, statement 2 is sufficient, and the answer is B.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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