Hi All,
We're asked if P is EVEN. This is a YES/NO question. We can solve it by TESTing VALUES. To start though, we have not been told ANYTHING about P, so it could be positive, negative, 0, an integer, a fraction, etc.
1) P^5 is EVEN
This tells us that P^5 could be any even number (re: -2, 0, 2, 4, 6, etc.)
IF....
P^5 = 32, then P = 2 and the answer to the question is YES.
P^5 = 2, then P = a non-integer and the answer to the question is NO.
Fact 1 is INSUFFICIENT
2) 142P - 82 = Even
With the equation in Fact 2, we're subtracting an even number (82) from 142P and getting an even number, thus 142P is EVEN.
IF....
142P = 142, then P = 1 and the answer to the question is NO.
142P = 284, then P = 2 and the answer to the question is YES.
Fact 2 is INSUFFICIENT
Combined, we know:
P^5 is even
142P is even
The only values that fit both Facts are even integers, so the answer to the question is ALWAYS YES.
Final Answer:
GMAT assassins aren't born, they're made,
Rich