A is the right answer.

ST-I since n^2/36 means n^2 is a multiple of 36 which in turn mean its a multiple of 6 and 6 is always divisible by 3

ST-II: 144/n^2 --- if n = 2 144 is divisible by 4 -- but 2 is NOT divisible by 4 - insuff

OA:A

In these kind of problems it is easier to plug numbers and find the answer

The Ques here asks whether POSITIVE integer n is divisible by 3
it means is n a multiple of 3 , such as 3,6,9,12....

Let us check statement 1:
n^2/36 is an integer.
this means n^2 is multiple of 36, such as 36,72 etc

let us find possible values of n which satisfy this equation
n can be 6,36 ...

We observe that n is a multiple of 3. Hence this statment alone can satify the equation.

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if that sounds complicated then let us consider factor of 36 =2*2*3*3
we observe that the first value of n^2 which we can safely assume has two 3's and two 2's in it
which means 'n' has atleast one 2 and one 3 in it.


Let us now consider statement 2 alone:
144/n^2 is an integer

let us start plugging values for n to satisfy this equation
n=1 satisfies , 144/1^2 = 144 , an integer
n=2 satisfies, 144 /4 = 36 , an integer
n=3 satisfies .....

This means n need not be a multiple of 3.
As we cant get a definite answer from this statement, this satement
cant answer our question alone.


ANS therefore is A: statement 1 alone is sufficient (2) alone is not sufficient