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
