Data Sufficiency

AAPL wrote:e-GMAT

A person invested $500 each in two different schemes S1 and S2. The return on investment will be calculated on compound interest, compounded annually. What is the difference in interest from S1 for 2nd year and S2 for 3rd year?

1) At the beginning of year 2, S1 amounts to $525.
2) At the end of year 1, S2 earns $25 more interest compared to S1.

OA C

Let's take each statement one by one.

Say the $500 invested in scheme S1 attracts an interest of R% per annum and the $500 invested in scheme S2 attracts an interest of r% per annum.

1) At the beginning of year 2, S1 amounts to $525.

=> 525 - 500 = $25 is the interest for one year in scheme 1. Thus, R = 10% p.a. However, we do not have any details about scheme S2. Insufficient.

2) At the end of year 1, S2 earns $25 more interest compared to S1.

Interest earned by S1 in one year = 500R/100 = 5R;
Interest earned by S2 in one year = 500r/100 = 5r

Thus, we have 5r - 5R = 25 => r - R = 5.

Can't get the unique values of r and R, thus, the answer. Insufficient.

(1) and (2) together

From R = 10% and r - R = 5, we have r = 15%.

Thus,

Interest from S1 for 2nd year = 525*10% = $52.5

Amount received from S2 after 3rd year = 500(1 + 15%)^3;
Amount received from S2 after 2nd year = 500(1 + 15%)^2

Interest from S2 for 3rd year = 500(1 + 15%)^3 - 500(1 + 15%)^2 = A unique value, say P

Thus, the difference in interest from S1 for 2nd year and S2 for 3rd year = P - 52.5 = A unique value. Sufficient.

There is no need to calculate the unique value till we are sure that we get a unique value.

The correct answer: C

Hope this helps!

-Jay
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