Official Solution:


(1) \(m\) is a multiple of 14. Not sufficient as no info about \(n\).

(2) \(n\) is a divisor of 14. Not sufficient as no info about \(m\).

(1)+(2) As from (2) \(n\) is a divisor of 14 then it must be a divisor of every multiple of 14, therefore it's a divisor of \(m\) too. Sufficient.


Answer: C
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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?

(2) says that n is a divisor of 14 but if n = 28, then it's not a divisor of 14, it's a multiple of 14.
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aah i get it now! thank you

Hi Bunuel,
Please confirm if the below is correct...
If it was given : m is not necessarily an integer then the answer would be E ?
My reasoning:
1) m could 14 x integer or
m could be 14 x 2.5

2 ) n = 2 or 7

Then by combining 1 and 2, m/n can still be fraction ( 2.5 in this case) hence E

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

I got this question wrong since I didn't think "Divisor" can refer to a "Factor".

From what I knew, a number divided by a divisor, may/may not yield a remainder. Doesn't say anything about the divisor being a factor.

Turns out a divisor and factor are the same

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


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The attempted questions should also show the answer test taker opted for initially when clicked on explanation. After a long test you don't remember what option you chose and it can help you assess your own mindset while making a particular mistake. But this should only be shown when clicked on explanation. otherwise, it needs to be hidden.

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

Please help me clear my confusion:
When statement 2 says that "'n' is a divisor of 14", why did we assume that it is a factor of 14 ?
since it is a divisor, it can or can not completely divide 14 or any of its multiples.

Any help would be appreciated.
Thanks in Advance!!

A divisor = a factor, it's an integer which divides another integer without a remainder.
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can n be equal to SQRT(14)?

No, because we are told that n is a positive integer, while \(\sqrt{14}\) is not.
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Please help me to understand why m and n cant be the below
m = 28 (multiple of 14)
n = 42 (divisor of 14)

Then m/n will be 2/3

42 is a multiple of 14, not a divisor. 14 is divisor of 42.
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We can pretty much tell we need to combine both statements :

m is at least 14. ( a positive multiple of 14)

n is a divisor of 14. So n can be 1,2,7,14. All of these 4 values will make m/n an integer.

Hence C
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