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

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### Top Member

Vincen Master | Next Rank: 500 Posts
Joined
07 Sep 2017
Posted:
458 messages
6

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

Tue Sep 12, 2017 10:39 am
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?

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
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Posted:
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GMAT Score:
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Sun Sep 17, 2017 10:20 am
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

Thanked by: Vincen

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