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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Divisible by 6?
Source: Beat The GMAT — Data Sufficiency |
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
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
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
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
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.
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.
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