Let the amount Ann deposited into the accounts A and B be \(a\) and \(b\) respectively.
Question: \(0.08b-0.05a=?\)

(1) Ann deposited $200 more in account B than in account A --> \(b=a+200\). Not sufficient.

(2) The total amount of interest that the two accounts earned in the first year was $120 --> \(0.05a+0.08b=120\). Not sufficient.

(1)+(2) We have two distinct, linear equations with two unknowns: \(b=a+200\) and \(0.08b+0.05a=120\), thus we can solve it and get the value of \(0.08b-0.05a\) (so save time, as no need of actual solving). Sufficient.

Answer: C.
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Account A earns 5 percent simple annual interest (Ra) and account B earns 8 percent simple annual interest(Rb).

Interest = (principal amount x rate x time in year) /100
interest calculated on A (Ia)= AxRaX1 /100 =0.05A
interest calculated on B (Ib)= BxRbX1 /100 =0.08B

form statement 1:
(1) Ann deposited $200 more in account B than in account A.
or, B-200 = A or, B-A = 200

putting B-A = 200 in above equation, we can get the interest in terms of A or B only.
so, we cannot find that how many dollars greater than the amount of interest that account A earned in the first year.

NOT SUFFICIENT

(2) The total amount of interest that the two accounts earned in the first year was $120.

Ia+Ib = 120
or, 0.05A + 0.08B = 120
we don't know the value of A & B . hence,
NOT Sufficient.

On combining both statement:
B-A = 200
& 0.05A + 0.08B = 120

here on solving, we can get individual value of A & B. and also the interest values.

Hence, Sufficient.

ANS IS C.

HOPE IT WILL

Yeah i didnt bother to solve either i just saw it was solvable and went for C

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

There are 3 variables (original money, interest rate, time period) in questions regarding compound and and simple accounts
For this question above, the time period is told to be 1 year, and the interest rates are told to be 5% and 8% respectively, so we only need to know the original money, which means there are 2 variables (A,B) and 2 equations are given by the 2 conditions, so there is high chance (C) will become the answer.
Looking at the conditions together, from B=A+200, A*5%+B*8%=120, we can derive an unique answer for the interests, so the conditions are sufficient and the answer becomes (C).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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My immediate reaction on this one was that you could solve with Statement one alone by

Difference in Interest Earned = Difference in Rate(Difference in Amount Invested) => .03(200) = $6.00

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.
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The target question: The difference between the interest of an account A and the interest of an account B?? (
The formula to find simple interest: I = Principal (P) * interest rate (%) * time

St1: Principal of an account B = 200 + Principal of an account A (Pb = 200 + Pa)
Ia = Pa * 5% *1 -->Pa = (Ia)/5%
Ib = Pb * 8% *1-->Ib = (200 + Pa) * 8% (1)
-->We know only Principal--> NS
St2: Ia + Ib = 120 (2)
No other info-->NS
St1 + St2: we have 2 equations with 2 unknown figures, so we can easily find the amount of interest in each account-->So, I choose C.

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