Jamboree and GMAT Club Contest: Is xy < 0?

tough and tricky one!


Is xy < 0?

this is a Yes/No DS question. In order to answer this question, we need to know the signs of X and Y. In order to satisfy this condition one must be positive and the other negative. Any other cases will yield a positive number

(1) -x + y > 5
from this, we can rearrange y>x+5. it can be the case that x=-3 and y>2 in this case, the answer is yes.
in the same time, x can be 1, and y must be greater than 6. in this case, we'll have a positive number, and the answer is no.

From the above said, statement 1 is insufficient.

(2) 3y - x < -9
rearrange: 3y < x-9
x can be 81, which means that 3y must be less than 72. Y must be less than 24. Since Y can be both positive and negative, statement 2 is insufficient.

We can now cross out answer choices A, B, and D, and if we don't know how to solve further, we can take a smart guess, with a chances of answering correctly 1/2.

let's take now 1+2:
y>x+5
3y<x-9
what can we do with this system of equations?
let's multiply first with -1. we get -y<x-5. Note that when multiplying with a negative number, the inequality sign switches. Since the inequality sign is the same, we can add both inequalities and still get the same result:
2y < -14, and Y < -7. Ok, now we know for sure Y is negative. But don't get excited. To answer the question, we need to know the sign for X as well.
TO find the sign for X, multiply the first equation with -3, and get -3y<-3x-15
again, add the 2 equations:
-3y<-3x-15
3y<x-9
we get:
0<-2x-24 or 24<-2x or 12<-x. Multiply this by -1, switch the inequality sign: -12>x. X is thus negative. Knowing the signs for X and Y, we can give a definite answer to the question.
the answer is thus C.