positive integers....2

[acorra]

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

A) 6

B) 12

C) 24

D) 36

E) 48

[kris610]

Given n is a positive integer.

The largest positive integer that would divide n is n itself.

Find n*n such that it is a multiple of 72 and is also a perfect square.

Of the given choices, 24 fits the bill.

[cramya]

https://www.beatthegmat.com/og-quant-rev ... 11652.html

[logitech]

Kris,

if n^2 is divided by 72, which is 2^3 x 3^2

The closest way to make this a perfect square is to multiply by 2

So N^2 = 144 and N: 12

so is the answer!

Given n is a positive integer.

The largest positive integer that would divide n is n itself.

Find n*n such that it is a multiple of 72 and is also a perfect square.

Of the given choices, 24 fits the bill.

[kris610]

Well..the question asks for the *greatest* possible number n such n^2 is a perfect square and is a multiple of 72.

Let's take n=24. 24^2 is divisible by 72 and is a perfect square.

Why is that not the answer?

[logitech]

Well..the question asks for the *greatest* possible number n such n^2 is a perfect square and is a multiple of 72.

Let's take n=24. 24^2 is divisible by 72 and is a perfect square.

Why is that not the answer?

well how about 48 ?

maybe there is a typo here ? Maybe the question is not asking the GREATEST because it does not make any sense. THE GREATEST NUMBER IS INFINITE!

[yezz]

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

A) 6

B) 12

C) 24

D) 36

E) 48

72 = 2^3*3^2

N^2 at least = 2^4*3^2

N is least = 2^2*3.....12

[kris610]

Well..the question asks for the *greatest* possible number n such n^2 is a perfect square and is a multiple of 72.

Let's take n=24. 24^2 is divisible by 72 and is a perfect square.

Why is that not the answer?

well how about 48 ?

maybe there is a typo here ? Maybe the question is not asking the GREATEST because it does not make any sense. THE GREATEST NUMBER IS INFINITE!

Logitech, the square of 48 is not a multiple of 72.

[Ian Stewart]

Well..the question asks for the *greatest* possible number n such n^2 is a perfect square and is a multiple of 72.

Let's take n=24. 24^2 is divisible by 72 and is a perfect square.

Why is that not the answer?

well how about 48 ?

maybe there is a typo here ? Maybe the question is not asking the GREATEST because it does not make any sense. THE GREATEST NUMBER IS INFINITE!

There's no typo. The question asks what the greatest integer is that *must* divide n, not what the greatest integer is that *could* divide n. Since n could be equal to 12, the answer certainly can't be 24 or 48, since 24 and 48 are not divisors of 12. I posted a solution in an earlier thread, which cramya linked to above. It's identical to yezz's solution above, but with a bit more detail.

[TrueLie]

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

A) 6

B) 12

C) 24

D) 36

E) 48

I have a problem with this kind of question. What does "the largest positive integer that must divide n" mean? Suppose that this "largest positive integer" is X. Hence, does the question mean "X is divisible by n" or "n is divisible by x"? If the second case is correct, that mean we can re-write the question as "If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that n must divide is:". Is this true?

I am not a native English speaker, that's why I have this problem.

Thank you.