Hi ash4gmat,
This really should have been posted in the DS Forum, but I'll be happy to walk you through it:
We're told that a Pierpont prime is any PRIME number p such that p = (2^K)(3^L)+1, where K and L are non-negative integers. We're told that R is an INTEGER. We're asked if R a Pierpont prime. This is a YES/NO question.
1) 1 < R < 5
From this Fact, R is limited to only 3 possibilities: 2, 3 and 4. We have to check to see if they fit the definition of a Pierpont prime...
IF...
R = 2, then K = 0 and L = 0 would give us R = (1)(1) + 1 = 2, so R IS a Pierpont Prime and the answer to the question is YES.
R = 3, then K = 1 and L = 0 would give us R = (2)(1) + 1 = 3, so R IS a Pierpont Prime and the answer to the question is YES.
R = 4, then the answer to the question is NO (since 4 is NOT a prime number)
Fact 1 is INSUFFICIENT
2) 0 < R < 4
This Fact also limits R to only 3 possibilities: 1, 2 and 3. Our prior work (in Fact 1, above) will be useful here...
IF....
R = 1, then the answer to the question is NO (since 1 is NOT a prime number)
R = 2 or R = 3, then the answer to the question is YES (the work above proves this).
Fact 2 is INSUFFICIENT
Combined, we know...
1 < R < 5
0 < R < 4
R can ONLY be 2 or 3. Since both of those numbers lead to the same "YES" answer, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
