Is 13 a factor of M? a) 117 M is the square of an integer b)

Question

Is 13 a factor of M?
a) 117 M is the square of an integer
b) M/117 is the square of an integer

OA is  D

bml · Answer

Is the question correct- option (b) is not clear?

hogann · Answer

B is not complete

However I believe A is sufficient.

A) Factors of 117 are 3,3 and 13. 
If 117M is a square it must contain the same Factors on both sides. Therefore to complete this we know that at least one factor of M is 13.
Sufficient

IanStewart · Answer

Technically, using Statement 1 alone, M could be something like 1/13, in which case M isn't even an integer. That said, on the real GMAT, if a question ever asks about the factors of a number M, the question will declare in advance that M is an integer, since otherwise the question would make no sense (it isn't meaningful to talk about the factors of a fraction).

GMAT TIGER · Answer

IMO:
In B,    K    that I added should be a multiple of M. If not, then B is irrelavant.

barakhaiev · Answer

What is the OA? Because I think it is  D .
1) sufficient. already discussed
2) sufficient too. if M/117 is a square of an integer, factors of M should be 3 and 13 as well.

Please post OA.

mnpqxyzt · Answer

a) 117M = 13*3^2*M = k^2
=> M = 13 * R^2 
=> sufficient

b) M/117 = k^2
=> M = 117 * k^2 = 13*3^2*k^2
=> 13 is a factor of M
=> sufficient

Ans: D

mnpqxyzt · Answer

The definition "factor" exists only with the integer, so M is obviously an integer.

chetan2u · Answer

"The definition "factor" exists only with the integer, so M is obviously an integer. ...."
 it would be an integer if it is given that M has factors....... there is a difference in...." is 13 one of the factors of M?" AND " Is 13 a factor of M"...

GmatNY86 · Answer

I was thinking D. BUT, it doesn't say that M is an integer.

So, let's start with 117=3^2*13

1) If M=0, then 117M=0. This is the square of 0, an integer (unless there's a special property I'm not aware of). 0 is not a factor of 13. Also if M=1/13, then 117M will be 9. 13 is not a factor of 1/13. For every positive power of 13 (and you would need a positive odd power to make this a square) M would be a multiple of 13. So since you can have 2 answers, A IMO is insufficient.

2) M/117 is a square of an integer. Once again, unless there's a special property that I'm not aware of, the smallest square of an integer is 0. 0 is not a factor of 13. However, once you got to the next largest, 1, you end up with 117, which is a multiple of 13 and every other possible quotient of M/17 thereafter is a multiple of 13.

3) Both answers give a possibility of 0, but also give a possibility of 117 for example.

So my answer is E.

Edit: I confused it as is 0 a factor of 13, and not if 13 is a factor of 0. I guess 0 has infinite factors since 0 is 0 multiplied by anything. But still, what if M is 1/13?

GmatNY86 · Answer

Forget it, it's all in the previous post.

Is 13 a factor of M? a) 117 M is the square of an integer b)

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