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

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SVP
Joined: 06 Sep 2013
Posts: 1651
Concentration: Finance
A $500 investment and a$1,500 investment have a combined  [#permalink]

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06 Oct 2013, 06:27
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Difficulty:

15% (low)

Question Stats:

84% (01:47) correct 16% (02:22) wrong based on 187 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

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Joined: 18 Dec 2012
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Concentration: General Management, Strategy
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Re: A $500 investment and a$1,500 investment have a combined  [#permalink]

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06 Oct 2013, 06:47
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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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Joined: 06 Sep 2013
Posts: 1651
Concentration: Finance
Re: A $500 investment and a$1,500 investment have a combined  [#permalink]

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06 Oct 2013, 07:31
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%
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Joined: 12 Jan 2013
Posts: 145
Re: A $500 investment and a$1,500 investment have a combined  [#permalink]

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29 Dec 2013, 04:35
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1
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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Joined: 26 Jul 2010
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Location: European union
Re: A $500 investment and a$1,500 investment have a combined  [#permalink]

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24 Mar 2015, 16:38
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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26 Jun 2017, 19:11
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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Joined: 28 Jun 2015
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Re: A $500 investment and a$1,500 investment have a combined  [#permalink]

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26 Jun 2017, 22:56
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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27 Jun 2017, 03:52
2
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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27 Jun 2017, 14:29
2
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%

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

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26 Dec 2017, 03:51
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.