From May 1 to May 30 in the same year,

Hi jjjinapinch,

We're told that from May 1 to May 30 in the same year, the balance in a checking account increased. We're asked for the balance in the checking account on May 30. This question is a great example of a 'concept' question, meaning that you don't have to do any actual math to solve it (as long as you recognize the concepts involved).

1) If, during this period of time, the increase in the balance in the checking account had been 12 percent, then the balance in the account on May 30 would have been $504

Fact 1 gives us a 'hypothetical' situation, that allows us to create the following equation:
(1.12)(May 1st balance) = $504

We can use this information to figure out the initial balance on May 1st, but since we don't know that ACTUAL increase in the balance of the account, we cannot determine the total in the account on May 30th.
Fact 1 is INSUFFICIENT

2) During this period of time, the increase in the balance in the checking account was 8 percent.

Fact 2 gives us the (percent) increase in the balance of the account, but we still don't know the ending balance on May 30th.
Fact 2 is INSUFFICIENT

Combined, we know:
-The balance on May 1st
-The balance increased by 8% from May 1st to May 30th

With this information, we CAN calculate the balance on May 30th (but we don't actually have to do any of the individual math 'steps' to know that).

Final Answer: C

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