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A $500 investment and a $1,500 investment have a combined ye [#permalink]
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09 Mar 2014, 15:07
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The Official Guide For GMAT® Quantitative Review, 2ND EditionA $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% Problem Solving Question: 143 Category: Algebra Percents Page: 80 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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09 Mar 2014, 15:08
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SOLUTIONA $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 8.57=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.
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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09 Mar 2014, 18:48
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Can be solved in 2 ways:
Fast method (Using ratios):
500$ & 1500 $ are in the ratio of 1:3
Since $500 gives a return on 7%, its 1.5 % away from 8.5%(the average return)
So ratio of returns of $500: $1500 should be in the ratio 3:1 deviation from 8.5%.
Therefore the return on $1500 = 8.5% + (1.5%/3) = 9%
Method 2  General Math
Total annual return on both @ 8.5% = $170
Return on $500 @ 7% = $35.
So return on $1500 = $170$35 = $135
Rate = (135/1500)*100 = 9%



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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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09 Mar 2014, 19:18
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(A) 9% Total Capital = 2000 Total Return @ 8.5 % = 170 Return from 500 is @ 7% = 35 Balance = 17035 = 135 Percentage = 100 * 135 / 1500 = 9
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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09 Mar 2014, 23:52
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Option A. 8.5% on 2000=170 Of ths 7% of 500 is one part and x% of 1500 is the other part 7% of 500=35 17035=135 x% of 1500=135 x=9



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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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11 Mar 2014, 02:53
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8.5  7 = 1.5 x  8 = 0.5 x = 9 How 0.5? Because the ratio is 1:3. Check Image Answer A Time Taken 00:45 Difficulty level 600
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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11 Mar 2014, 03:10
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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 5/8% (D) 11% (E) 12%
Sol: Given that (1500+500)*(8.5%)= $170 Total return and $500 has yearly return of 7% or 500*7/100 =$35...So remaining $135 is the return on Investment of $1500 so we have 1500*a/100=135 or a=135*100/1500 > a =9% Ans is E 600 level is okay
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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11 Mar 2014, 08:06
X017in wrote: So ratio of returns of $500: $1500 should be in the ratio 3:1 deviation from 8.5%.
Can someone elaborate this part please ?



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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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15 Mar 2014, 00:39
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lool wrote: X017in wrote: So ratio of returns of $500: $1500 should be in the ratio 3:1 deviation from 8.5%.
Can someone elaborate this part please ? It is given that the $500 investment is 1.5% BELOW the average. Which means that the $1500 investment has to be X% above average to balance the combined interest of 8.5% 500 * 1.5 = 1500 * X X = (500 / 1500) * 1.5 X = (1/3) * 1.5 > This can be rewritten as X/1.5 = 1/3, which is the ratio that is mentioned above X = 0.5% above the average Ans = 9%



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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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15 Mar 2014, 09:54
SOLUTIONA $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 8.57=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.
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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22 Apr 2014, 00:24
Hi Bunuel,
Could you please explain me the highlighted part "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 8.57=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."
Though i understood the basic math approach, i am unable to understand in ratio approach.
Help is appreciated . Thanks in advance ;



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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]
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14 Jul 2016, 08:49
2000x0.85=0.7x500+15x x=135/15=9% A is the answer Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionA $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% Problem Solving Question: 143 Category: Algebra Percents Page: 80 Difficulty: 650 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!



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A $500 investment and a $1,500 investment have a combined ye [#permalink]
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14 Oct 2017, 16:45
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionA $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% Two amounts with two different weights and rates contribute to an overall rate of return on their combined amount Straight weighted average A = $500 portion B = $1500 portion r = interest rate \((A_{r}*A_{amt})+(B_{r}*B_{amt}) = (A+B)_{r}* (A+B)_{amt}\)\((.07)(500) + (\frac{x}{100})(1500)= (.085)(2000)\) \(35 + 15x = 170\) \(15x = 135\) \(x = \frac{135}{15} = 9\) The interest rate for the $1,500 portion is 9 percent Answer A
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