We can use even/odd number properties to solve this question

even * even = even
even * odd = even
odd * odd = odd

even +/- even = even
even +/- odd = odd
odd +/- even = odd
odd +/- odd = even

Statement 1

P^5 = P*P*P*P*P. Using even * even = even and odd * odd = odd, if P^5 is even , if P is an integer, P must also be even.

HOWEVER, we do not know that P is an integer. This is an easy assumption to make (I made the same assumption on first glance!). This means that P^5 could could be, say 4, making $$P = \sqrt[5]{4} =1.31950791...$$ All such non-integer options for P that make P^5 even will come out as irrational numbers (a decimal that cannot be written as a fraction). So P can be either an even integer or an irrational number. Insufficient.

Statement 2

If 142P - 82 is even, and 82 is even, then 142P must also be even (based on even +/- even = even and odd +/- even = odd). If 142 * P is even, and 142 is even, then P can be even or odd (based on even * even = even and even * odd = even). Insufficient

Note: If 142P - 82 is even and thus a whole number, then 142 * P must be an integer. This means that P must either be an integer itself OR possibly a fraction like 1/2. This means that P cannot be an irrational number.

Both

Statement 1 tells us that P must be an even integer or an irrational number. Statement 2 tells us that P must be an even integer, and odd integer, or a fraction. The only option that satisfies both statements is an even integer. Sufficient.

Hi VJesus12,

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: C

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