Is p^2 > q^2 ?

1. p > 0
2. q > 0

(C) 2008 GMAT Club - m02#11

The given statement simplifies to:
p^2 - q^2 > 0

The real question, then is this: is (p + q) (p-q) > 0 ? The statements taken together allow for p > q and p < q , which makes the sign either positive or negative.

Source: GMAT Club Tests - hardest GMAT questions

I don't understand the answer. Could someone break it down further please?

p^2 - q^2 > 0



1) p>0

p^2 - q^2 ---> +ve when p>q (assume q is also positive)
p^2 - q^2 ---> -ve ve when p<q (assume q is also positive)


two solutions insuffcient

2) q>0

p^2 - q^2 ---> +ve when p>q (assume p is also positive)
p^2 - q^2 ---> -ve when p<q (assume p is also positive)

two solutions insuffcient

combine.
p>0 q>0 AND DON'T know the proper relation between p and q
p>q q>p

p^2 - q^2 --> lead +ve or -ve values depends on p>q or q>p
insuffcient

E.

p^2 > q^2 ? can be rephrased as |p| > |q| ?

1. p > 0
Doesn't give any information on relationship between absolute values of p and q

2. q > 0
Doesn't give any information on relationship between absolute values of p and q

1 & 2 Combined also doesn't give any information on the relationship.

Hence E.

Yeah I think you're just overthinking it.

In order to know whether p^2 > q^2 we have to know something about the relationship between p and q -- that one is larger than the other, that one is negative and one is positive, that one is less than 1 and the other isn't, etc.

Neither of the two statements separately nor the two statements combined give you any information about this.

Making a little change in question, say:

2. q < 0

The answer would still be E

Actually I wouldn't take the pains of factorizing and all that .. keeping it simple

Square of any number is positive .. so unless the answer choices help establishing a relationship between p and q it's impossible to say which is greater. Hence the option E.