BengalScientist wrote:
BengalScientist wrote:
Is P + Q > 1/P + 1/ Q?
1) P < Q < 1
2) PQ < 1
1) P < Q < 1
2) PQ < 1
I simplified the equation as P + Q > (Q + P)/PQ , PQ>1
Statement 2 is sufficient.
What am i missing here? can some one unfreeze my brain please...
Firstly,you cannot cancel out the factor (P+Q) as because it can be zero also. Secondly, even if (P+Q) is not zero,you cannot cross multiply the term PQ as because you don't know about its sign. When PQ<1, PQ can be positive or negative. Had the 2nd fact statement read as PQ>1, then we could have easily cross multiplied. Thus, the correct inequality to solve would be -->Is (P+Q)(1-1/PQ)>0.
From F.S 1, for P = -1/2 and Q = 1/2, P+Q = 1/P+1/Q = 0. Thus, we get a NO for the question stem. But for P=-1/2 and Q = -1/4, P+Q(-3/4) is greater than 1/P+1/Q(-6). Thus , we get a YES for the question stem. Thus, this fact statement is Insufficient.
From F. S 2, we can take the exact 2 sets of values for P and Q as above and clearly this fact statement is also Insufficient.
Taking both together, we again have no NEW information.Insufficient.
E.
