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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

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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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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I think this is a high-quality question and I agree with explanation.
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Hi @banuel,

When a statement says "x is a multiple of a number", do we or do we not consider 0 a possibility (for x)?
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Hi @banuel,

When a statement says "x is a multiple of a number", do we or do we not consider 0 a possibility (for x)?

Yes, 0 is a multiple of every integer. a is a multiple of b means that \(a = x*b\) for some integer x (the multiplier) and since we can express 0 as 0 = 0*(any integer), then 0 is a multiple of every integer. For example, 0 = 0*5, thus 0 is a multiple of 5 or 12 = 4*3, thus 12 is a multiple of 3.

Having said that, for this question, neither m nor n can be 0 because we are told that m and n are positive, while 0 is neither positive nor negative number.
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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