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

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

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New post 09 Mar 2014, 15:07
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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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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]

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New post 09 Mar 2014, 15:08
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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.
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]

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New post 09 Mar 2014, 18:48
1
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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New post 09 Mar 2014, 19:18
1
(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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New post 09 Mar 2014, 23:52
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
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]

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New post 11 Mar 2014, 02:53
4
8.5 - 7 = 1.5
x - 8 = 0.5
x = 9

How 0.5? Because the ratio is 1:3. Check Image

Answer A
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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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New post 11 Mar 2014, 03:10
1
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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New post 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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New post 15 Mar 2014, 00:39
1
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%
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]

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New post 15 Mar 2014, 09:54
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.
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 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 8.5-7=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 ;
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Re: A $500 investment and a $1,500 investment have a combined ye [#permalink]

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New post 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 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.

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

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New post 14 Oct 2017, 16:45
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

Answer A
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A $500 investment and a $1,500 investment have a combined ye   [#permalink] 14 Oct 2017, 16:45
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