Is p q ? (1) p^2 q^2 (2) p^3 q^3

Question

Is p > q ?

(1) p^2 > q^2
(2) p^3 > q^3

Bunuel · Answer

Is p > q ? (1) p^2 > q^2 Take the square root: |p| > |q|. This means that p is further from 0 than q is, which is clearly insufficient to answer the question whether p > q. (2) p^3 > q^3 Take the cube root: p > q. Sufficient. Answer: B. P.S. Manipulating Inequalities (adding, subtracting, squaring etc.). P.P.S. Please name topics properly. Check rule 3 here: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.

GmatDM2016 · Answer

consider negative range to find extreme scenarios
A) p^2 > q^2
Insufficient as 
q can be 2 while p can be -3 still satisfying equation 9> 4 but -3 < 2
also q can be 2 and p can be 3 satisfying equation 9> 4 also 3> 2
Squares hide the original sign

B) if p =-2 and q= -3
p^3 = -8
q^3 = -27 
-8 > -27 and -2 > -3 therefore p > q
Also, p=2 , q=-3 then 8> -27 therefor p>q

similarly if we choose one + one -ve to satisfy the equation, we will get p>q 
similar behavior for fractions.

hence B

MathRevolution · Answer

Condition 1) p^2 - q^2 > 0 (p+q)(p-q) > 0 p + q > 0 implies p - q > 0 or p > q . p - q < 0 implies p - q < 0 or p < q . Thus we have p = 2 , q = 1 and p = -2 , q = -1 . Thus this condition is not sufficient. Condition 2) p^3 > q^3 p^3 - q^3 = (p-q)(p^2+pq+q^2) > 0 Without loss of generality, we can assume q e 0 . p^2 + pq + q^2 = q^2 \{ \frac{p^2}{q^2} + \frac{p}{q} + 1 \} = q^2 \{ (\frac{p}{q})^2 + 2(\frac{1}{2})(\frac{p}{q}) + 1 \} = q^2 \{ (\frac{p}{q})^2 + 2(\frac{1}{2})(\frac{p}{q}) + \frac{1}{4} + \frac{3}{4} \} = q^2 \{ ( \frac{p}{q} + \frac{1}{2} )^2 + \frac{3}{4} \} \ge \frac{3}{4} q^2 > 0 Thus we have p^2 + pq + q^2 > 0 . Since p^3 - q^3 > 0 , p^2 + pq + q^2 > 0 and p^3 - q^3 = (p-q)(p^2 + pq + q^2) > 0 , we have p - q > 0 or p > q . This is sufficient. Answer: B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is p > q ? (1) p^2 > q^2 (2) p^3 > q^3

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