Janice made three investments totaling $5,000. In the first year the

Question

Janice made three investments totaling $5,000. In the first year the investments earned 6 percent, 8 percent, and 9 percent interest, respectively. Which of the following could be the total amount of interest earned on the three investments that year?

I. $475
II. $425
III. $335

A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III

I. $475
II. $425
III. $335

A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III

I understand the correct answer but i took too much time solving as I keep picking numbers after making the necessary adjustments in the equations. Does anyone has any tips in solving this faster?

Thank you in advance!!

gmatophobia · Accepted Answer

Maximum Possible Interest

Janice earns maximum interest if she invests all the amount at a 9% rate of interest.

Max Interest earned =  \frac{5000 * 9 * 1}{100} = $450

Minimum Possible Interest

Janice earns minimum interest if she invests all the amount at a 6% rate of interest.

Min Interest earned =  \frac{5000 * 6 * 1}{100} = $300

Hence the interest Janice earns will be between $300 and $450.

$300 <   Interest Earned  < $450

From the given options, II and III satisfy the value range.

Option D

emont · Answer

are there similar questions like this please?

Bunuel · Answer

Yes, you can check similar questions under Percent and Interest Problems tag here: https://gmatclub.com/forum/search.php?s ... tag_id=191 Hope this helps.

JoeSal · Answer

I have a question on this. Why do we assume that it will be all 9%, or all 6%? From the question, I'm assuming that it really is 6%, 8%, and 9% per part of the 5000.

bhavanadandu · Answer

We are essentially maximizing and minimizing returns on that 5000. Max would be 9% on all of 5k amount and Min would be 6% on all of 5k amount. This gives us a range for the "could be" question, elimination 475 as a possible answer. Rest 2 fall within this limit.

KarishmaB · Answer

The question is a theoretical application of weighted averages. The total principal is $5000. Assuming almost the entire amount is invested at 6% (and very little at other two percentages), the interest earned will be about 6/100 * 5000 = $300 Assuming almost the entire amount is invested at 9% (and very little at other two percentages), the interest earned will be about 9/100 * 5000 = $450 The interest will be somewhere in between these two. Hence II and III both are possible. Answer (D) Discussion on weighted averages: https://www.youtube.com/watch?v=_GOAU7moZ2Q

axeofflane · Answer

Yes its so simple, but i got stuck up on divisibility

Janice made three investments totaling $5,000. In the first year the

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