Hi rohankant12,
This question can be solved by TESTing VALUES.
We're asked for the value of X.
Fact 1: X:Y = 3:11
This ratio gives us a 'relationship' between X and Y, but does not tell us what either variable is. We know that X MUST be a multiple of 3 and Y MUST be an equivalent multiple of 11, but we don't have the actual numbers.
IF....X=3, Y=11, then the answer is 3
IF....X=6, Y=22, then the answer is 6
Fact 1 is INSUFFICIENT
Fact 2: The least common multiple of X and Y equals three times the value of Y
You might need to 'play around' with this Fact to figure out the pattern involved. From Fact 1, I'm thinking that we should look for X as a multiple of 3, so I'll start there...
IF...X = 3, then the LCM of X and Y has to be 3 TIMES the value of Y....
IF....X=3, Y=1, then the LCM is 3 (which is 3 times the value of Y) and the answer to the question is 3
IF....X=6, Y=2, then the LCM is 6 (which is 3 times the value of Y) and the answer to the question is 6
Fact 2 is INSUFFICIENT
Combined, we have evidence that X can likely be at least 2 different outcomes (3 or 6), but we have to incorporate all of the given information to prove it:
X = 3, Y = 11.... this fits the ratio 3:11 and the LCM is 33 (which is the value of 3Y).
X = 6, Y = 22.... this ratio (6:22) reduces to 3:11 and the LCM is 66 (which is the value of 3Y).
Combined, INSUFFICIENT
Final Asnwer:
As an aside, what is the source of this question?
GMAT assassins aren't born, they're made,
Rich