Hi Gmat_mission.
In this DS question, all we need to see is if we are able to find the balance in the checking account on May 30. Let's take a look at the statements.
Statement 1:
(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
First, notice that this statement tells us the balance on May 30. But this is just a supposition. So, actually, we don't know what is the balance on May 30.
Here, we could find what was the balance on May 1, but we don't know what is the actual percent increase. Therefore, this statement is
NOT SUFFICIENT.
Statement 2:
(2) During this period of time, the increase in the balance in the checking account was 8 percent.
Now, we are told the actual percent increase, but we don't know how much money was in the account on May 1, so we can't determine what is the balance on May 30. Therefore, this statement is
NOT SUFFICIENT.
Statement 1 + Statement 2:
(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
(2) During this period of time, the increase in the balance in the checking account was 8 percent.
Using the first statement, we can know how much money was in the account on May 1.
Let \(I\) be the balance in the checking account on May 1. Here, we are told that $$I+12\%\cdot I=504\ \ \ \Rightarrow\ \ 1.12I=504\ \ \Rightarrow\ I=450.$$ On the other hand, the second statement tells us that the increase was 8%, so on May 30 there will be
$$Final=I+8\%\cdot I=450+8\%\cdot450=450+36=486\ dollars$$ Therefore, using both statements together is
SUFFICIENT.
Hence, the correct answer is the option
_C_.
I hope it helps you. <i class="em em-sunglasses"></i>
