Source: Official Guide Revised GRE 1st Ed. Part 6; Set 2; #4

1

# x2y > 0 xy2 < 0

x2y > 0 xy2 < 0 Quantity A : x Quantity B : y Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

### 2 Explanations

1

Jose Veloz

Hi guys!
I solved this one following one rule when solving inequalities which is "only odd numbers (powers) remain".
This rule says that if you multiply or divide by a square, the sign of the inequality won't change direction. Because x2 is always positive.
For example if i have x3>0, divinding by x2, we'll get x>0
Hence we simplified the inequality and now we only want to know if x>0

On the OG exercise, applying the mentioned rule, we get:

x2y>0 (only odd remain), hence we only are left with: y>0

The 2nd inequality, xy2<0, we simplify and get: x<0
We inmediatly know that x<0, and y>0, and B is greater than A

Mar 10, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Jose! Nice work! That is an excellent use of that rule :D Thanks for sharing your alternative approach to this practice problem!

4 Chris Lele, Magoosh Tutor

Oct 7, 2012 • Comment