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12...n can be 12 or 144, etc..12 divides 144 as well as 12 but 144 divides 144 but not 12. so 12 is the largest integer for the statement to be true... _________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

12...n can be 12 or 144, etc..12 divides 144 as well as 12 but 144 divides 144 but not 12. so 12 is the largest integer for the statement to be true...

12...n can be 12 or 144, etc..12 divides 144 as well as 12 but 144 divides 144 but not 12. so 12 is the largest integer for the statement to be true...

Cris ... you are too good.

Answer is indee 12.

nakib, isn't 24 larger than 12 and doesn't n=24 satisfy the conditions? What is the source and OE?
If you got the answer choices and 12 is the only one in them that is a multiple of 12, then ..

nakib, isn't 24 larger than 12 and doesn't n=24 satisfy the conditions? What is the source and OE?

looks like question is asking the maximum positive integer that divide ANY n. So for example, if n = 12, n^2 = 144 which is divisible by 72 but 24 does not divide 12 i still believe question could have been more clear.

True 24 does not divide 12.

"If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is"

n=24 is a +ve integer
n^2 = 576 and (n^2)/72 = 8 -> so divisible by 72
n=24 holds true for the conditions and the largest number that can divide 24 is 24.
That's why I think we just need the answer choices.