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Intern  Joined: 08 Feb 2008
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If m and n are nonzero integers, is m/n an integer?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 74% (01:25) correct 26% (01:33) wrong based on 253 sessions

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If m and n are nonzero integers, is m/n an integer?

(1) 2m is divisible by n

(2) m is divisible by 2n
Manager  Joined: 04 Feb 2007
Posts: 68
Re: Can someone explain this to me  [#permalink]

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1) 2m is divisible by n
this is the same as saying 2 * (m/n) is an integer.
but m/n in this case does not have to be an integer for 2m/n to be an integer. try m=1, n=2 then try m=2,n=1.

-> insufficient.

2) m is divisible by 2n
this is the same as saying (1/2) * (m/n) is an integer

if one-half of (m/n) is an integer, then twice that will have to be integer.

try any numbers that satisfy the condition m/2n is an integer if you want to check it.

-> sufficient
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Re: Can someone explain this to me  [#permalink]

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Completely agree with firasath
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Re: Can someone explain this to me  [#permalink]

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firasath wrote:
1) 2m is divisible by n
this is the same as saying 2 * (m/n) is an integer.
but m/n in this case does not have to be an integer for 2m/n to be an integer. try m=1, n=2 then try m=2,n=1.

-> insufficient.

2) m is divisible by 2n
this is the same as saying (1/2) * (m/n) is an integer

if one-half of (m/n) is an integer, then twice that will have to be integer.

try any numbers that satisfy the condition m/2n is an integer if you want to check it.

-> sufficient

I disagree.
I think both are insufficient by themselves or even if taken together.

For case 2, what if m = 24, n = 36. m is divisible by 2n=72. But, m/n is not an integer.

We don't know if the coefficients of the multiples of m or n are divisible even if we take both statements together.
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Re: Can someone explain this to me  [#permalink]

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For case 2, what if m = 24, n = 36. m is divisible by 2n=72. But, m/n is not an integer.

hey Krishna do you mean that 24 is divisible by 72 ??
I think u assumed that that 72 is divisible by 24 which is not what is asked.
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Re: Can someone explain this to me  [#permalink]

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thinkbigthink800 wrote:
For case 2, what if m = 24, n = 36. m is divisible by 2n=72. But, m/n is not an integer.

hey Krishna do you mean that 24 is divisible by 72 ??
I think u assumed that that 72 is divisible by 24 which is not what is asked.

Crap! Thank you. You're right. I would have got this question wrong for sure if it's on the test.
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Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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Well, I used prime boxes to do that one.

So, m,n are NOT zero and we are asked is $$\frac{m}{n}$$ has a remainder of zero. So, n should be a factor of m or m should be a multiple of n.

 is the first prime box.
We see that the elements or factos of n belong to 2m. But m has also a 2. This means that m alone may not be able to cover n. So, in other words, it might be the 2 that makes m a factor of n.

For example:
2m=10 would make m = 5. And let's say that n=2.

Then 2m/n= 10/10 = 1. Great, but:
m/n = 5/2 = 2.5. Not that great...

 is the second prime box.
We see that all of n is covered by m. This is sufficient, because all of the factors of n are also factors of m.

So, ANS B
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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1
Hi All,

Questions that involve factors and multiples are essentially about patterns, so TESTing VALUES is a great approach (and once you can prove the pattern, then you can stop working). In these situations, it's important to be thorough (and make sure that you consider the simplest ideas first).

Here, we're told that M and N are NON-0 INTEGERS. We're asked if M/N is an integer. This is a YES/NO question.

Fact 1: 2M is divisible by N.

IF....
M = 1
2 is divisible by N

IF....
N = 1
then M/N = 1/1 and the answer to the question is YES.

N = 2
then M/N = 1/2 and the answer to the question is NO.
Fact 1 is INSUFFICIENT.

Fact 2: M is divisible by 2N

IF....
M = 2
2 is divisible by 2N
N = 1
then M/N = 2/1 and the answer to the question is YES.

IF...
M = 4
4 is divisible by 2N

N = 1
then M/N = 4/1 and the answer to the question is YES.

N = 2
then M/N = 4/2 and the answer to the question is YES.

You should notice the pattern here. Since the question asks us to focus on M/N....if M is divisible by 2N, then it WILL be divisible by N.
Fact 2 is SUFFICIENT.

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Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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divanshuj 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

Statement 1

2m/n =

2(m)= n x k - k meaning some random integer

insuff

Statement 2

m= k x 2(n)
m/n = k x 2

suff
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Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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For st 2:- what if M= 2 and n =3 Therefore m/2n is integer but m/n is not..
Can anyone pls explain
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Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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swetafuria wrote:
For st 2:- what if M= 2 and n =3 Therefore m/2n is integer but m/n is not..
Can anyone pls explain

If m = 2 and n = 3, then m/(2n) = 2/6 = 1/3, which is not an integer.
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Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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Exactly..so both the statements are insufficient..Then answer should be not B
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Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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swetafuria wrote:
Exactly..so both the statements are insufficient..Then answer should be not B

Not clear what you mean.

(2) says: m is divisible by 2n, so $$\frac{m}{2n} =integer$$ --> $$\frac{m}{n} =2*integer=integer$$. Sufficient.
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Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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divanshuj 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

As I could draw from the question, statement 2 means that m is always greater than n and m is a multiple of n. That's why it is sufficient.
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Re: If m and n are nonzero integers, is m/n an integer?  [#permalink]

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_________________ Re: If m and n are nonzero integers, is m/n an integer?   [#permalink] 09 Oct 2019, 02:10
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