Divisible by 6?

[gmatblood]

Is the positive integer n divisible by 6?

1) n^2/180 is an integer
2) 144/n^2 is an integer

IMO: D

[rijul007]

Is the positive integer n divisible by 6?

1) n^2/180 is an integer
2) 144/n^2

IMO: D


Is the red part also an integer?

[rijul007]

is n divisible by 6?
Rephrased ques..
Is n divisible by both 2 and 3?


Statement 1
n^2/180 is an integer
This means n should be divisible by all prime factors of 180(which are 2,3,and 5)

Hence n is divisible by 2 and 3 both.

Sufficient

[rijul007]

Statement 2

we cant conclude anything from this expression

if 144/n^2 is an integer

12 is divisible by all prime factors of n
value of n could be => 1, 2, 3, 4, 6 or 12


if 144/n^2 is not an integer

we cant conclude anything about n


Hence, Insufficient

Option A

[gmatblood]

Is the positive integer n divisible by 6?

1) n^2/180 is an integer
2) 144/n^2

IMO: D


Is the red part also an integer?

Sorry.. yes 2) is also an integer

[rijul007]

gmatblood wrote:
Sorry.. yes 2) is also an integer

Then my ans is A

What is OA?

[user123321]

1) n^2/180 = integer
the least value of n^2 = 900 where in which n to be +ve integer.
Rest of the values for n^2 are nothing but perfect squares where 36 is a default factor
so n = 30k is div by 6.
hence sufficient.
2) In second one
say if n is 1
then 144/1^2 = integer but 1 is not divisible 6
say if n is 6
then 144/6^2 = integer but 6 is divisible by 6
hence insufficient.