If \(m\) and \(n\) are positive integers is \(\frac{m}{n}\) an integer?


(1) \(m\) is a multiple of 14

(2) \(n\) is a divisor of 14
_________________

I got E for this question. Followed the below approach.
What if we consider m=14 and n=28 => Not an integer
If m=28, n=28 => integer.

What did i do wrong?

aah i get it now! thank you

I'm quite sure that 2.5 x 14 is no valid multiple of 14

Statement 1:
m = 14k, where k is a positive integer. Can't say if m/n is an integer since 14/3 is not an integer and 14/7 is an integer.

Statement 2:
n is a divisor of 14. This means n can be 1, 2, 7 or 14. But the statement alone does not tell us about m/n. m/n could be 5/7 (is not an integer) or 14/7 (is an integer).

Statements 1+2:

m = 14k and n=1,2,7 or 14. For all the 4 values of n, m/n is an integer. Hence this is sufficient to answer weather m/n is an integer.
Hence answer is C


----- Crave Your Rave -------

I think this is a high-quality question and I agree with explanation.

A divisor = a factor, it's an integer which divides another integer without a remainder.
_________________

No, because we are told that n is a positive integer, while \(\sqrt{14}\) is not.
_________________

42 is a multiple of 14, not a divisor. 14 is divisor of 42.
_________________