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2) The total amount of interest that the two accounts earned in the first year was $120. OA C ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 2008 messages Followed by: 31 members Upvotes: 470 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 $120. OA C Say Ann deposited$A in Account A and $B in Account B. Thus, she earned 5A/100 =$A/20 in the first year from Account A and earned 8B/100 = $2B/25 in the first year from Account B. We have to get the value of 2B/25 - A/20. Let's take each statement one by one. 1) Ann deposited$200 more in account B than in account A.

Thus, 2B/25 - A/20 = 2(A + 200)/25 - A/20 = 2A/25 - A/20 + 16 = 3A/100 + 16. We don't have the value of A. Insufficient

2) The total amount of interest that the two accounts earned in the first year was $120. => 2B/25 + A/20 = 120 Can't get the unique value of 2B/25 - A/20. Insufficient. (1) and (2) together From (2), we have 2B/25 + A/20 = 120; plugging-in the value of B = A + 200, we get 2(A + 200)/25 + A/20 = 120 2A/25 + 16 + A/20 = 120 13A/100 = 104 A =$800 and B = 800 + 200 = $1,000 Thus, 2B/25 - A/20 = (2*1,000)/25 - 800/20 =$40. Sufficient.

Hope this helps!

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

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 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$$0.05\left(B-200\right)+0.08B=120\ 0.05B-10+0.08B=1200.05B+0.08B=120+100.05B+0.08B=130\frac{0.13B}{0.13}=\frac{130}{0.13}B=1000\ dollar0.05A+0.08\left(1000\right)=1200.05A=120-80\frac{0.05A}{0.05}=\frac{40}{0.05}A=800\ dollarsSI\ for\ A\ =0.05\cdot800SI\ for\ B=0.08\cdot1000Difference=\ 80-40=\ 40\ dollar$$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

### GMAT/MBA Expert

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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.

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