Is positive integer n divisible by 3?

[vrajesh.dave]

Is positive integer n divisible by 3?

(1) n^2/36 is an integer

(2) 144/n^2 is an integer


OA: A

Can someone please walk me through this one.

[nitin_prakash_khanna]

All question stem tells us is that n is a positive integer.

Statement 1:
n^2 / 36 is an integer.

Prime factors of 36 will be
36 = 2^2 * 3^2

For n^2 divided by 36 to be an integer n will have to have either one 3 or 3^2 in its prime factor.
In both the cases n will be divisible by 3.

So This is Sufficient.

Statement 2 Tells that 144 / n^2 is an integer.
prime representation of 144 = 2^4*3^2

now assume n has only 3 in its prime factorization then 144 / n^2 will be integer and n will be divisible by 3.

But on the other hand if n has only 2 or 2^2 in its prime factorization then 144 / n^2 will still be integer but n will not be divisible by 3.

So INSUFFICIENT

Hence Answer A.

Can you confirm OA?

[RonPurewal]

Is positive integer n divisible by 3?

(1) n^2/36 is an integer

(2) 144/n^2 is an integer


OA: A

Can someone please walk me through this one.

nitin's solution, above, is good.

regarding statement (2):
if you see a statement that implies a SMALL NUMBER OF POSSIBILITIES, then you should just enumerate all the possibilities.

statement 2 is just 1, 2, 3, 4, 6, 12. this is something you could figure out fairly quickly. (you should DEFINIELY have all the perfect squares up to 144 committed to memory; preferably, in fact, you'll know all of them up to 25^2 = 625.)

if you find that list, it's pretty clear that 1, 2, 4 are "no"s and 3, 6, 12 are "yes"s. therefore #2 is insufficient.

[mark.hartmann]

All question stem tells us is that n is a positive integer.

Statement 1:
n^2 / 36 is an integer.

Prime factors of 36 will be
36 = 2^2 * 3^2

For n^2 divided by 36 to be an integer n will have to have either one 3 or 3^2 in its prime factor. --> Why will n either have one 3 or 3^2 in its prime factor? What about the 2s?!
Hope the questions does not reveal my beginner level to much :)
In both the cases n will be divisible by 3.

So This is Sufficient.

Statement 2 Tells that 144 / n^2 is an integer.
prime representation of 144 = 2^4*3^2

now assume n has only 3 in its prime factorization then 144 / n^2 will be integer and n will be divisible by 3.

But on the other hand if n has only 2 or 2^2 in its prime factorization then 144 / n^2 will still be integer but n will not be divisible by 3.

So INSUFFICIENT

Hence Answer A.

Can you confirm OA?

[tim]

it also has 2's, but we're not concerned with those because the question asks about 3..