# Shouldnt the 1st statement be sufficient? Since we can form the list {….-16,-8,-4,-2,2,4,8,16….} & so can definitely say that 12 isn’t in the list

K is a set of numbers such that

i) If x is in K, then -x is in K, and

ii) if each of x and y is in K, then xy is in K.

Is 12 in K?

(1) 2 is in K.

(2) 3 is in K.

Hi Nirvan,

I can understand your logic.

But don’t you think, by your logic, answer should be D(Each alone sufficient).

So, lets see what you have mistaken here,

Statement I says that 2 is in the set K, but it didn’t say only 2 or powers of 2 there.

For example, Its like I m saying student X studying in the class, but does it mean that only that student studying in the class. No right ?

So given that, 2 is there in the set,

so obviously according to the 1st condition, -2 is in the set,

and according to the second condition, -4 is in the set, we can build up on this saying 4 also in the set , it keep goes on.

We cant conclusively say whether 12 will be there in the set or not,

If there is 6 in the set, then we could have 12 using the second condition. It’s like may or may not be.

So nothing conclusive.

So statement I is insufficient.

Similar reasoning for statement II,

Together of course sufficient,

Because we will get a 12 using the I and II condition in the question.

So the answer is C.

Hope this helps.