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Divisible by 6?

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Divisible by 6?

by gmatblood » Sun Nov 06, 2011 11:06 am
Is the positive integer n divisible by 6?

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

IMO: D
Last edited by gmatblood on Sun Nov 06, 2011 1:53 pm, edited 1 time in total.
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Source: — Data Sufficiency |
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by rijul007 » Sun Nov 06, 2011 11:32 am
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?
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by rijul007 » Sun Nov 06, 2011 11:37 am
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
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by rijul007 » Sun Nov 06, 2011 11:41 am
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
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by gmatblood » Sun Nov 06, 2011 1:53 pm
rijul007 wrote: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
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by rijul007 » Sun Nov 06, 2011 2:08 pm
gmatblood wrote:
Sorry.. yes 2) is also an integer

Then my ans is A

What is OA?
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by user123321 » Sun Nov 06, 2011 4:42 pm
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.
Just started my preparation :D
Want to do it right the first time.
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