Please explain this some again in detail. I wasnt able to understand the explanation, probably with numbers substituted. Thanks.

If there is any specific step in any reasoning above, let me know, and I'll go over it again.

There can be NO shortcuts for statement (2) by considering some specific values, because this statement gives us enough information to proof that n²ª is a multiple of mª for ANY positive integers.

However, you can try a simpler case, let's say for a = 1. The explanation is the same, just put 1 instead of a, whenever you meet it. The question itself will become:

If m and n are positive integers, is n² a multiple of m? (1) n is a multiple of m/2 (2) n is a multiple of 2m

In your explanation of why answer A is insufficient, you give 2 examples of why the answer is no, which is an answer. You might include an example of when the answer is yes sometimes and no other times, making A insufficient.

Can you expand on the second point? I understand why if 2m is a divisor of n, then m is a divisor of n – but how do we get from there to understanding that n²ª is a multiple of m²ª?

statement 1) first statement needs to be an integer as n is a multiple of m/2

First statement is not a number. However you can say that n, m/2 and n / (m/2) must be integers, according to definitions of divisibility and a multiple.

Quote:

so if you write it as n/(m/2) = 2(n/m) and this needs to be an integer for it to be an integer we have two options:

thus n/m can be 1/2 -> not an integer NO or n/m can be 1,2,3,4,.......---> integers yes

thus Not sufficient

You are making the conclusion of whether n²ª is a multiple of mª or not, based on n/m . But it is NOT correct.

n/m can be a fraction, while n²ª will be a multiple of mª . Take, for example, n = 2 and m = 4. n/m = 1/2 – a fraction n²ª = 4ª is divisible by mª = 4ª

Quote:

statement 2) it states that n/2m is an integer

now separate it as (1/2) * (n/m) and this is an integer

thus for this to be an integer naturally (n/m) has to be an integer which cancels out the 2 in the denominator------> yes only

Thus statement 2 is sufficient as if n is multiple of m then n^2 will also be a multiple of m

This reasoning is correct. For formality, just add the last step. n² is a multiple of m, so (n²)ª is a multiple of (m)ª .

On the GMAT, would the number 7 be considered a multiple of the number 3.5? I am wondering, whether when picking numbers for this problem, I could have picked n = 7 and m = 7 (since n is multiple of m/2, and 7 is (or not?) a multiple of 3.5)

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