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A $500 investment and a $1,500 investment have a combined

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A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 06 Oct 2013, 05:27
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Difficulty:

  15% (low)

Question Stats:

85% (01:47) correct 15% (02:22) wrong based on 186 sessions

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A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

(A) 9%
(B) 10%
(C) 10\(\frac{5}{8}\)%
(D) 11%
(E) 12%

Suggested time: 30 seconds

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-500-invest ... 68574.html
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 06 Oct 2013, 05:47
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jlgdr wrote:
A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

(A) 9%
(B) 10%
(C) 10\(\frac{5}{8}\)%
(D) 11%
(E) 12%

Suggested time: 30 seconds


The equation we can form the question :

Return on Total Investment = Sum of individual Investments

\((500+1500) (8.5) = (500*7) + (1500x)\), where x is the return on investment of 1500.

Solving the equation, we get x = 9% ( Option A )
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 06 Oct 2013, 06:31
jlgdr wrote:
A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

(A) 9%
(B) 10%
(C) 10\(\frac{5}{8}\)%
(D) 11%
(E) 12%

Suggested time: 30 seconds


We can also try differentials approach. -1.5+3y=0. Then y=0.5. So 8.5%+0.5%=9%
Answer (A)
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 29 Dec 2013, 03:35
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jlgdr wrote:
A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

(A) 9%
(B) 10%
(C) 10\(\frac{5}{8}\)%
(D) 11%
(E) 12%

Suggested time: 30 seconds



1% of 2000 = 20.. 8.5% of 2000 = 170.

1% of 500 = 5 and 7% of 500 = 35..

170 - 35 = 135 ----> 135/1500 = 9*15/100*15 = 9/100, hence answer A.

This took me closer to 90 secs rather than 30.
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 24 Mar 2015, 15:38
500/ (500+1500) * 7 + 1500 / (500+1500) * x = 8.5

1.75 + 3/4 * x = 8.5

3/4 x = 6.75

x = 9

Took me about 2 minutes though.
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 26 Jun 2017, 18:11
2
Alternative 30-second approach:

The $500 and $1500 investments are in the ratio 1:3, hence the $1500 investment is responsible for 3/4 of the total investment returns. We know the total average return is 8.5% and the $500 investment yields a 7% return, which is 1.5% away from the average.

Hence, the $1500 must be 1/3 of the distance away from the average as compared to the $500 investment. 1/3 of 1.5% is 0.5%.

8.5% + 0.5% = 9%. Answer: A.
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 26 Jun 2017, 21:56
x - 8.5/(8.5-7) = 1/3
3x - 25.5 = 1.5
3x = 27
x = 9. Ans - A.
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 27 Jun 2017, 02:52
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jlgdr wrote:
A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

(A) 9%
(B) 10%
(C) 10\(\frac{5}{8}\)%
(D) 11%
(E) 12%

Suggested time: 30 seconds


Total principal \(= 500 + 1500 = $2000\)

Combined return on Principal is 8.5% = 8.5% of 2000 \(= \frac{8.5}{100}* 2000 = 170\)

Interest received on $500 is 7% = 7% of 500 \(= \frac{7}{100}* 500 = 35\)

Let rate of interest on $1500 be \(x\).

Total interest received = Interest received on $500 + Interest received on $1500

\(170 = 35 + (\frac{1500 * x}{100})\)

\(170 = \frac{3500 + 1500*x}{100}\)

\(17000 = 3500 + 1500*x\)

\(1500* x = 17000 - 3500\)

\(x = \frac{13500}{1500} = 9\)%. Answer (A) ...
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 27 Jun 2017, 13:29
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A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?

Total Amount = $500 + $1,500 = $2,000

Interest on Total Amount:

\(= 2000 * \frac{8.5}{100}\)

\(= $170\)

Interest Amount on $500 \(= 500 * \frac{7}{100}\)

\(= $35\)

Interest Amount for $500 + Interest Amount for $1500 = Interest Amount for $2000

35 + Interest Amount for $1500 \(= 170\)

Interest Amount for $1500 \(= 170 - 35\)

Interest Amount for $1500 \(= 135\)

135 is what % of 1500?

\(= \frac{135}{1500} * 100\)

= 9%

Hence, Answer is A
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Re: A $500 investment and a $1,500 investment have a combined  [#permalink]

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New post 26 Dec 2017, 02:51
A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1 ,500 investment have?

(A) 9%
(B) 10%
(C) 10 5/8%
(D) 11%
(E) 12%

The ratio of investments is 500:1,500 = 1:3.

The deviation from the average return from $500 investment and $1,500 investment must be in the ration 3:1.

$500 investment return has the deviation from the mean of 8.5-7=1.5%, thus $1,500 investment return must have the deviation from the mean equal to 0.5%, which means that $1 ,500 investment has 8.5+0.5=9% yearly return.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-500-invest ... 68574.html
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Re: A $500 investment and a $1,500 investment have a combined &nbs [#permalink] 26 Dec 2017, 02:51
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