Hi All,

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

Final Answer:

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

Rich

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