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

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.

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.

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.

[1] 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...

[2] 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

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.

Final Answer:
GMAT assassins aren't born, they're made,
Rich

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

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.

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.

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.

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

(1) 2m is divisible by n
2m/n is an integer
If m=3: n=2; 2m is divisible by n but m/n =3/2 = 1.5 is NOT an integer
But if m=6;n=2; 2m is divisible by n and m/n =6/2 = 3 is an integer
NOT SUFFICIENT

(2) m is divisible by 2n
m/2n is an integer
m/n is an integer
SUFFICIENT

IMO B

Given: m and n are not zero and are integers.
To find: m/n = Integer ie is m divisible by n

1. 2m is divisible by n
This could mean that m is divisible by n or n = 2
Not sufficient

2. m is divisible by 2n
For m to be divisible by 2n, it needs to be either m=2n or m=2n x (some other number)
In both cases we can see that m is divisible by n
Hence sufficient
Hence B