If p5 and q-2, then which of the following is always true?

Question

If p > 5 and q > -2, then which of the following is always true? A) pq > -10 B) pq < -10 C) -p < 2q D) -p > 2q E) pq > 10

Bunuel · Answer

If p > 5 and q > -2, then which of the following is always true? A) pq > -10. If p = 100 and q = -1, then pq = -100 < -10. So, this option is not always true. B) pq < -10. If p = 100 and q = 0, then pq = 0 > -10. So, this option is not always true. C) -p < 2q. This is the same as p + 2q > 0. We have p > 5 and 2q > -4 (multiplied by 2) Add: p + 2q > 1. So, p + 2q is greater than 0. So, this option is always true. D) -p > 2q. Above we got that -p < 2q, so this is not true. E) pq > 10. If p = 100 and q = 0, then pq = 0 < 10. So, this option is not always true. Answer: C.

KarishmaB · Answer

p > 5 p = 6, 7, 8, 9, 10, 11, 12, ... q > -2 q = -1, 0, 1, 2, 3, 4, 5, ... A) pq > -10 If p = 11, q = -1, then pq = -11. Not always true. B) pq < -10 If p = 6, q = -1, then pq = -6. Not always true. E) pq > 10 If p = 6, q = 0, then pq = 0. Not always true. C) -p < 2q p is positive. Divide both sides by 2p to get -1/2 < q/p Looks like it might be true based on some values of p and q we have taken above. Let's hold on to it and check the leftover option. D) -p > 2q Divide both sides by 2p to get -1/2 > q/p If q = -1 and p = 6, we get -1/2 > -1/6 which is not true. So (C) must always be true. We don't need to worry about non-integer values of p and q.

spetznaz · Answer

+1 for option C.
In addition to solutions above , one could also arrive at C in the following way:
-p<-5; -2q<4
-p-2q<-1 --> -p<2q-1 which means , -p<2q.
Hence option C

LeoN88 · Answer

For me it took some time but successfully negated A B D E

A p=17, q=-1
B p=17, q=1
D for q=0
E for q=0
Answer  C

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.

If p>5 and q>-2, then which of the following is always true?

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

GMAT Problem Solving (PS) Questions