Data Sufficiency

23. Last year Luis invested x dollars for one year, half at 8 percent simple annual interest and the other half at 12 percent simple annual interest. Now he wants to reinvest the x dollars for one year in the same two types of investments, but the lower rate has decreased. If the higher rate is unchanged, what fraction of the x dollars must he reinvest at the 12 percent rate so that the total interest earned from the x dollars will be the
same for both years ?

(1) The lower rate is now 6 percent.
(2) The total amount of interest earned from the two investments last year was $3,000.


Hi,
the answer is A) but can anyone explain how to get the number of fraction that should be invested to 12percent rate??

Hi

I worked that out as under:

First we need to know the return percentage on the investment x is the first scenario

x/2*8/100 + x/2*12/100 gives us 10x/100. Hence we know the return expected on the total investment is 10%.

Now considering (1), we know that the rates are 6% and 12% and we need to know the fraction of investment made in 12%.

Here let the amount invested in 6% be y and 12% be z. Then we get

6y/100+12z/100=(y+z)10/100

This when simplified gives 2y=z. This means that z should be 2/3rd of the total investment getting 12% return.

I am not sure whether this is the best way to do this but the result looks accurate.

Prasanna

That's certainly how to get there algebraicaly. The key thing to remember on Data Sufficiency is that we don't always need to be able to actually solve, we just need to know when we could solve. If you know the interest rates on the two investments, you can figure out the ration necesscary to get a particular return (in this case an average return of !0%).

If, when you're working on a problem, you're not sure how to do something algebraicaly, plug in numbers and figure out an answer that way. It can hep sometimes to see these things as more concrete.