Is x + y xy? (1) x 0 y (2) |y| = x I know

Question

Is x + y > xy?

(1) x > 0 > y

(2) |y| = x

I know that this can be simple when we experiment with numbers. However, I want to avoid experimenting because I can tell that there is a subtle message in the inequality Is x + y > xy. Would anyone please show how we could abstractly interpret it without doing much math? I know that it's possible, but I just couldn't figure it out in this question.

Thanks

amitdgr · Answer

1) x > 0 > y means x is +ve and y is -ve so xy will be -ve also from x > 0 > y we get x+(-y)>0 so x-y > xy ( +ve > -ve) 1 is sufficient 2) |y| = x now x can be y or -y if x=y then x+y is 2x or 2y and xy = x^2 or y^2 2x < x^2 or x+y < xy if x=-y then -y+y = 0 and xy is -ve x+y > xy 2 not sufficient Answer is A ? What am I missing ?

spriya · Answer

1)x>0>y => x+y>xy say x=1,y=-2 => x+y=-1 > -2 x+y x+y=-1.5 < -1 INSUFFI 2) |y|=x => x is +ve and and x=value of y where y is +ve or -ve say y=2 x+y =xy y=x=3 => x+y INSUFFI 1) and 2) now y<0 and x=|y| => y=-1 x=1 x+y>-1 y=-0.5 x=0.5 x+y>xy always since x+y=0 xy <0 IMO C

scthakur · Answer

The two statements are essentially saying that x and y are equidistant from 0 on the number line and y is to the left and x is to the right.

Hence, x + y will always be zero and xy will be -ve.

However, if x and y are not equidistant then depending upon the absolute value of x or y (whether less than 1 or more than 1), the values of x+y and xy will be different (less or more).

Hence, C is the answer.

tarek99 · Answer

exactly! statement 2 tells us that x can ONLY be a zero and positive, while y can be either positive, a zero, or even negative. When you look at statement 1, when combining the 2 statements, it says that x and y aren't zero, while statement 2 says that both x and y have the same absolute value, which helps us to approach this inequality.

Is x + y > xy? (1) x > 0 > y (2) |y| = x I know

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards