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Math Expert V
Joined: 02 Sep 2009
Posts: 58344
A $500 investment and a$1,500 investment have a combined ye  [#permalink]

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Question Stats: 86% (01:58) correct 14% (02:42) wrong based on 448 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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%

Problem Solving
Question: 143
Category: Algebra Percents
Page: 80
Difficulty: 650

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Math Expert V
Joined: 02 Sep 2009
Posts: 58344
Re: A $500 investment and a$1,500 investment have a combined ye  [#permalink]

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SOLUTION

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. _________________ General Discussion Current Student Affiliations: CA, SAP FICO Joined: 22 Nov 2012 Posts: 32 Location: India Concentration: Finance, Sustainability GMAT 1: 620 Q42 V33 GMAT 2: 720 Q47 V41 GPA: 3.2 WE: Corporate Finance (Energy and Utilities) Re: A$500 investment and a $1,500 investment have a combined ye [#permalink] Show Tags 3 Can be solved in 2 ways: Fast method (Using ratios): 500$ & 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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2
(A) 9%

Total Capital = 2000

Total Return @ 8.5 % = 170

Return from 500 is @ 7% = 35

Balance = 170-35 = 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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1
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
170-35=135
x% of 1500=135
x=9
Manager  Joined: 25 Sep 2012
Posts: 232
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GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34 Re: A $500 investment and a$1,500 investment have a combined ye  [#permalink]

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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

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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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 _________________ “If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.” Intern  Joined: 30 Jan 2014 Posts: 12 Re: A$500 investment and a $1,500 investment have a combined ye [#permalink] Show Tags 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 ? Intern  Joined: 28 Jan 2014 Posts: 13 Location: India GMAT 1: 740 Q49 V41 Re: A$500 investment and a $1,500 investment have a combined ye [#permalink] Show Tags 2 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 re-written as X/1.5 = 1/3, which is the ratio that is mentioned above X = 0.5% above the average Ans = 9% Math Expert V Joined: 02 Sep 2009 Posts: 58344 Re: A$500 investment and a $1,500 investment have a combined ye [#permalink] Show Tags SOLUTION 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.

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

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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 8.5-7=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 ." Though i understood the basic math approach, i am unable to understand in ratio approach. Help is appreciated . Thanks in advance ; Intern  Joined: 02 Jul 2014 Posts: 9 Location: India Concentration: Technology, Strategy Schools: ISB '17, IIMA , IIMB, Mannheim, EBS, XLRI GMAT Date: 08-16-2015 GPA: 2.69 WE: Design (Manufacturing) Re: A$500 investment and a $1,500 investment have a combined ye [#permalink] Show Tags 2000x0.85=0.7x500+15x x=135/15=9% A is the answer Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND Edition 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% 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 Project Each 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! Senior SC Moderator V Joined: 22 May 2016 Posts: 3538 A$500 investment and a $1,500 investment have a combined ye [#permalink] Show Tags Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND Edition 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% 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

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

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Use weighted average formula:

$$\frac{w1}{w2}=\frac{Avg2 - Avg}{Avg - Avg1}$$

$$\frac{500}{1500}=\frac{x - 8.5}{8.5 - 7}$$

$$\frac{1}{3}=\frac{x - 8.5}{1.5}$$

$$1.5 = 3x-25.5$$

$$27 = 3x$$

$$9 = x$$
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Re: A $500 investment and a$1,500 investment have a combined  [#permalink]

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