Kelly invested in two different funds, Fund F and Fund M

Question

Kelly invested in two different funds, Fund F and Fund M. For each $100.00 invested in Fund F, Kelly earned $8.50 in interest the first year. For each $100.00 invested in Fund M, Kelly earned $7.60 in interest the first year. If Kelly earned 8.2 percent in interest from the two investments that year, what dollar amount was invested in Fund M?

(1) The amount invested in Fund F was $20,000 more than 50 percent of the total amount invested.

(2) The amount invested in Fund F was $80,000.

Hi chetan2u
would be really helpful if you could explain this part
Ratio of funds F and M = FM=8.2−7.6 / 8.5−8.2

Thanks

egmat · Accepted Answer

Here is a  detailed video solution  for this interesting question.
See how this question can be solved in the test environment using " Owning the Dataset " approach.

https://www.youtube.com/watch?v=vlfGmEpTiNA

Let us know if you have any questions.

chetan2u · Answer

Beware of C trap.
 You have two quantities, and the relation in two is given in one statement and the other gives you the value of 2nd quantity. First can be found.

Let us solve the question

Kelly invested in two different funds, Fund F and Fund M. For each $100.00 invested in Fund F, Kelly earned $8.50 in interest the first year. For each $100.00 invested in Fund M, Kelly earned $7.60 in interest the first year. If Kelly earned 8.2 percent in interest from the two investments that year, what dollar amount was invested in Fund M?

Let us simplify the main statement

8.2 per 100$ is nothing but % return.
Fund...............F.........AVG.......M
%interest.......8.5.........8.2......7.6

By weighted average method,
  Ratio of funds F and M =  \frac{F}{M}=\frac{8.2-7.6}{8.5-8.2}=\frac{0.6}{0.3}=\frac{2}{1} , that is F=2M

(1) The amount invested in Fund F was $20,000 more than 50 percent of the total amount invested. 
 F=\frac{50}{100}*(F+M)+20000=2M.........2F=F+M+40000.......F=M+40000........2M=M+40000......M=40000 
Suff

(2) The amount invested in Fund F was $80,000. 
F=2M........2M=80000......M=40000
Suff

D

Bunuel · Answer

Kelly invested in two different funds, Fund F and Fund M. For each $100.00 invested in Fund F, Kelly earned $8.50 in interest the first year. For each $100.00 invested in Fund M, Kelly earned $7.60 in interest the first year. If Kelly earned 8.2 percent in interest from the two investments that year, what dollar amount was invested in Fund M?

We are given that Fund F earns an annual 8.5% and Fund M earns an annual 7.6%, while together they earn 8.2%. This implies that we can get the ratio of the amount invested in Fund F to the amount invested in Fund M: F/M (assuming $F was invested in Fund F and $M was invested in Fund M).

(1) The amount invested in Fund F was $20,000 more than 50 percent of the total amount invested.

The above implies that F = 0.5(F + M) + 20,000. Together with knowing F/M, we'd have two distinct linear equations with two unknowns, which means that we can solve for both. Sufficient.

(2) The amount invested in Fund F was $80,000.

This gives the value of F. So, knowing F/M, we can get the value of M. Sufficient.

Answer: D.

As we can see, we can solve this question in 30 seconds without any algebra.

P.S. If still interested in knowing how to get F/M, here it is: 8.5/100*F + 7.6/100*M = 8.2/100*(F + M) gives F = 2M.

getsetfly · Answer

chetan2u

Ratio of funds F and M = FM=8.2−7.6 / 8.5−8.2

can you please explain this part

thanks

monkinaferrari · Answer

Hi  chetan2u 
would be really helpful if you could explain this part 
Ratio of funds F and M = FM=8.2−7.6 / 8.5−8.2

Thanks

ShilpiAgnihotrii · Answer

Hey, its the concept of weighted average, pls go through the post by Karishma and Bunuel on GMAT club for better understanding.

purplelemonsoda · Answer

"(1) The amount invested in Fund F was $20,000 more than 50 percent of the total amount invested."

I interepreted it as: "(1) The amount invested in Fund F was ($20,000 more than) (50 percent of the total amount invested)."
so: 20,000 MORE THAN 0.5 (M+F), so 20,000 + 0.5 (m+f) NOT 20,000 + 1.5 (m+f)

why is everyone thinking of it as 1.5* and not just 50* (m+f)

KarishmaB · Answer

Responding to a pm: How does one know that weighted average can be used here? Fund F - $8.5 for every $100. This means that rate of interest for fund F = 8.5% Fund M - $7.6 for every $100. This means that the rate of interest for fund M = 7.6% Total interest rate earned = 8.2% Hence we see that some money was invested at 8.5% and some at 7.6% to give us an overall rate of 8.2%. Hence we should use weighted averages here. What will be the weights? We need to average interest rate. Interest rate = Interest/Principal Since Principal is in the denominator, it means the weights are the principal amounts. Hence the ratio will give us the ratio of money invested in the two funds. \frac{w1}{w2 }= \frac{(A2 - Avg)}{(Avg - A1)} = \frac{(7.6 - 8.2)}{(8.2 - 8.5)} = \frac{2}{1} = \frac{F}{M} Hence F = 2M (1) The amount invested in Fund F was $20,000 more than 50 percent of the total amount invested. F = 20,000 + \frac{(M+F)}{2} We have 2 distinct equations and 2 unknowns. We can solve for M. Sufficienct alone. (2) The amount invested in Fund F was $80,000. We have the value for F so we can get M. Sufficienct alone. Answer (D) Video on Weighted Averages: https://www.youtube.com/watch?v=_GOAU7moZ2QWhat are the weights in Weighted Avg: https://anaprep.com/arithmetic-weights-in-weighted-average/

Rahulkhera · Answer

Hi  Bunuel . I believe statement 1 equation should be F = 0.5(F+M) + 20000 and not 1.5(F+M) + 20000. Can you please confirm.

Bunuel · Answer

_________________
Yes, correct.

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Kelly invested in two different funds, Fund F and Fund M

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