Data Sufficiency

GMAT Prep

Ann deposited money into two new accounts, A and B. Account A earns 5 percent simple annual interest and account B earns 8 percent simple annual interest. If there were no other transactions in the two accounts, then the amount of interest that account B earned in the first year was how many dollars greater than the amount of interest that account A earned in the first year?

1) Ann deposited $200 more in account B than in account A.
2) The total amount of interest that the two accounts earned in the first year was $120.

OA C

$$SI=\frac{PRT}{100}$$
$$For\ account\ A,\ SI=\frac{ART}{100}=\frac{\left(A\cdot5\cdot1\right)}{100}=0.05A$$
$$For\ account\ B;\ SI=\frac{BRT}{100}=\frac{\left(B\cdot8\cdot1\right)}{100}=0.08B$$

Statement 1
Ann deposited 250 dollars more in account B than account A
$$B-200=A$$
$$B=A+200$$
$$SI\ for\ A\ =\ 0.05A=0.05\cdot\left(B-200\right)$$
$$=0.05B-10\ $$
$$Value\ of\ A<B\ still\ remains\ unknown$$
Statement 1 is INSUFFICIENT.

Statement 2
The Total amount of interest in the two accounts in the first year was 120 dollars.
(S.I for A) + (S.I for B) = 120 dollars
0.05A + 0.08B = 120 dollar
Value of A and B are not given, hence statement 2 is INSUFFICIENT.

Combining both statement together
0.05A + 0.08B = 120 dollars ----- statement 2
where A = B - 200 -----statement 1
$$0.05\left(B-200\right)+0.08B=120\ $$
$$0.05B-10+0.08B=120$$
$$0.05B+0.08B=120+10$$
$$0.05B+0.08B=130$$
$$\frac{0.13B}{0.13}=\frac{130}{0.13}$$
$$B=1000\ dollar$$
$$0.05A+0.08\left(1000\right)=120$$
$$0.05A=120-80$$
$$\frac{0.05A}{0.05}=\frac{40}{0.05}$$
$$A=800\ dollars$$
$$SI\ for\ A\ =0.05\cdot800$$
$$SI\ for\ B=0.08\cdot1000$$
$$Difference=\ 80-40=\ 40\ dollar$$
Interest in account B for first year is 40 dollar greater than interest in Account A
Both statement together are SUFFICIENT.

$$Answer\ is\ Option\ C$$

AAPL wrote:GMAT Prep

Ann deposited money into two new accounts, A and B. Account A earns 5 percent simple annual interest and account B earns 8 percent simple annual interest. If there were no other transactions in the two accounts, then the amount of interest that account B earned in the first year was how many dollars greater than the amount of interest that account A earned in the first year?

1) Ann deposited $200 more in account B than in account A.
2) The total amount of interest that the two accounts earned in the first year was $120.

What is the value of 0.08B - 0.05A?

Statement 1:
B-A = 200
B = A+200

Case 1: A = $100 and B=$300, with the result that 0.08B - 0.05A = 0.08(300) - 0.05(100) = 24-5 = 19
Case 2: A = $200 and B=$400, with the result that 0.08B - 0.05A = 0.08(400) - 0.05(200) = 32-10 = 22
Since 0.08B-0.05A can be different values, INSUFFICIENT.

Statement 2:
0.05A + 0.08B = 120
No way to determine the value of 0.08B-0.05A.
INSUFFICIENT.

Statements combined:
Since we have two variables (A and B) and two distinct linear equations (B-A=200 and 0.05A + 0.08B = 120), we can solve for the two variables.
Thus, the value of 0.08B-0.05A can be determined.
SUFFICIENT.

The correct answer is C.