Night reader wrote:@ankur, this DS has certain conditions. If x is in K then x and -x are in K. We are given one number in statement (1) 2 and one number in statement (2) 3. Either of these numbers are x OR y. We cannot say 2=x=y when we do not know about the existence of the second variable (x OR y). Each condition implies only one number - so one variable x OR y!

now set K according to statement (1) has only x and -x {-2; 2}

according to statement (2) set K has only y or -y {-3; 3}

you cannot say xy in statement 1 and 2, because we have only one value for either x OR y.

if you combine both you get x*y {-6;-3;-2;2;3;6} there's no 12 ans answer No st(1&2) Sufficient

please read the previous posts, it's not the matter of personal like or dislike - just knowledge man

K is a set of numbers such that if x is in K, then -x is in K, and 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

The question in this problem is very straightforward. K is a set of numbers, please note the set K contains only x and y, BUT x and y are assigned values, otherwise how we know where does 12 come? OK? now we are looking up statement (1) and it says 2 is in K. what is 2? it's either x or y, whichever you like... So let's assign x=2, then how will set K look like? reread the problem "K is a set of numbers such that if x is in K, then -x is in K, and if each of x and y is in K, then xy is in K" Therefore, K should include 2 and -2, that's it! K E {-2;2} we stop here as statement (1) doesn't help us to solve this problem and locate 12, and we look ahead for statement (2). Statement (1) Is Not Sufficient;
Statement (2) 3 is in K --> y=3 OR K E {-3;3} again no trace of 12. Not Sufficient.

Let's combine statements (1&2): we should get x*y for set K here --> {-2;2} U {-3;3} --> how many ways we can arrange our set K? use counting actually 2*2 + 2 (plus two more values from each set, because we have values +/- ve sign) --> {-6; -3; -2; 2; 3; 6} that's it! Sufficient

this is Yes/No question, hence combined statements (1&2) are sufficient to answer NO. It's just C because we can answer No.

OneTwoThreeFour wrote:K is a set of numbers such that if x is in K, then -x is in K, and 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


I would love to hear your rationale on this question. Personally, I find the solution to be a bit puzzling.