• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

# Forum: If p and q are positive integers, is p > q?

If p and q are positive integers, is p > q?

(1) 4p + 5q = 87
(2) p^3 < 40q

OA is C.

Is any of the statements sufficient?

### GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
9765 messages
Followed by:
487 members
2867
GMAT Score:
800
Hi Vincen,

We're told that P and Q are POSITIVE INTEGERS. We're asked if P is greater than Q. This is a YES/NO question. This question can be solved by TESTing VALUES.

1) 4P + 5Q = 87

While this equation might look a bit difficult to deal with, the fact that P and Q must be POSITIVE INTEGERS significantly limits the possible solutions. With a bit of 'brute force' you can find the first two solutions (and then spot a pattern that will help you to find the other two solutions).

IF....
P = 3, Q = 15 then the answer to the question is NO
P = 8, Q = 11 then the answer to the question is NO

At this point, you should notice that you had to increase P by 5 to find the second solution. If you try that again, you'll find the 3rd and 4th solutions:

P = 13, Q = 7 then the answer to the question is YES
P = 18, Q = 3 then the answer to the question is YES
Fact 1 is INSUFFICIENT

2) P^3 < 40Q

Only one of the solutions above 'fits' Fact 2: P = 3, Q = 15 and the answer to the question is NO

IF...
P = 2, Q = 1 then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, there's only one solution that 'fits' BOTH Facts: P = 3, Q = 15, so the answer to the question is ALWAYS NO.
Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### Top First Responders*

1 Jay@ManhattanReview 79 first replies
2 Brent@GMATPrepNow 61 first replies
3 fskilnik 58 first replies
4 GMATGuruNY 37 first replies
5 ceilidh.erickson 12 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik

GMAT Teacher

207 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

148 posts
3 Scott@TargetTestPrep

Target Test Prep

105 posts
4 Jay@ManhattanReview

Manhattan Review

97 posts
5 GMATGuruNY

The Princeton Review Teacher

93 posts
See More Top Beat The GMAT Experts