A person invested $500 each in two different schemes S1 and

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Fri Jun 28, 2019 2:44 am

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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 interests 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

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Source: e-GMAT

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 28, 2019 2:44 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sat Jul 20, 2019 10:55 pm

Question=> Find the difference between the interest earned from S1 for the 2nd year and from S2 for the 3rd year.
Statement 1=> At the beginning of year 2, S1 amounts to $525. This means that principal + interest at the end of year 1 = $525
The exact value of rate of S2 is unknown, hence, statement 1 is NOT SUFFICIENT.

Statement 2=> At the end of year 1, S2 earns $25 more interest compared to S1.
Let interest for S1 and S2 = r1 and r2. $$\left(500\cdot\frac{r2}{100}\right)-\left(500\cdot\frac{r1}{100}\right)=25$$
The exact values of r1 and r2 is unknown, hence, statement 2 is NOT SUFFICIENT

Combining both statement together;
$$\left(500\cdot\frac{r2}{100}\right)-\left(500\cdot\frac{r1}{100}\right)=25$$
$$5r2-5r1=25\ \left(divide\ all\ through\ by\ 5\right)$$
$$r2-r1=5$$
Since, r1=5
r2 = 5 + 5
There both statements combined together ARE SUFFICIENT

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