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# Quentin put an amount of money into each of two new investments, X and

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Math Expert
Joined: 02 Sep 2009
Posts: 64216
Quentin put an amount of money into each of two new investments, X and  [#permalink]

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16 Jul 2017, 23:12
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Difficulty:

55% (hard)

Question Stats:

65% (02:45) correct 35% (02:53) wrong based on 74 sessions

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Fresh GMAT Club Tests' Question:

Quentin put an amount of money into each of two new investments, X and Y. Investment X pays x% simple annual interest and investment Y pays y% simple annual interest. After 1 year, the average (arithmetic mean) interest earned by investments X and Y was 7.6%. If x and y are consecutive positive integers, in that order, what fraction of the total amount was put in investment X?

A. 1/5
B. 1/3
C. 2/5
D. 3/5
E. 2/3

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Posts: 38
Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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16 Jul 2017, 23:55
2
x and y are consecutive integers where x<y and their weighted mean is 7.6%. So, x=7% and y= 8%.
Let amount invested in X = a
Let amount invested in Y = b
Simple Interest = ((amount invested)*(rate of interest)*(time))/100

Here, time = 1 year.
Interest from X = 0.07a
Interest from Y = 0.08b
Average Interest = 0.076(a+b)

0.076(a+b) = 0.07a + 0.08b
7.6a + 7.6b = 7a + 8b
0.6a = 0.4b
1.5a = b

We need to find a/(a+b)
= a/(a+1.5a)
= 2/5

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Joined: 28 Jun 2015
Posts: 272
Concentration: Finance
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Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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17 Jul 2017, 02:34
3
Bunuel wrote:

Fresh GMAT Club Tests' Question:

Quentin put an amount of money into each of two new investments, X and Y, that pay simple annual interest. Investment X pays x% simple annual interest and investment Y pays y% simple annual interest. After 1 year, the average (arithmetic mean) interest earned by investments X and Y was 7.6%. If x and y are consecutive positive integers, in that order, what fraction of the total amount was put in investment X?

A. 1/5
B. 1/3
C. 2/5
D. 3/5
E. 2/3

Since the mean of $$x$$ and $$y$$ is $$7.6$$, the only possible choice for $$x$$ and $$y$$ is $$7$$ and $$8$$, respectively.

Interest earned from investments $$X$$ and $$Y$$ after a year are $$0.07X$$ and $$0.08Y$$, respectively. Interest earned on the whole equals $$0.076(X+Y)$$.

So, we have: $$0.076(X+Y) = 0.07X + 0.08Y$$

$$0.076X - 0.07X = 0.08Y - 0.076Y$$

$$0.6X = 0.4Y$$

$$3X = 2Y$$

$$\frac{X}{X+Y} = \frac{X}{X+(3X/2)} = \frac{2X}{5X} = \frac{2}{5}.$$

Ans - C.
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Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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17 Jul 2017, 03:08
Bunuel wrote:

Fresh GMAT Club Tests' Question:

Quentin put an amount of money into each of two new investments, X and Y, that pay simple annual interest. Investment X pays x% simple annual interest and investment Y pays y% simple annual interest. After 1 year, the average (arithmetic mean) interest earned by investments X and Y was 7.6%. If x and y are consecutive positive integers, in that order, what fraction of the total amount was put in investment X?

A. 1/5
B. 1/3
C. 2/5
D. 3/5
E. 2/3

Hi..
We can also use weighted average method...
Since average interest is 7.6 and two interest x and y are consecutive integers, they are 7 and 8 respectively..

Now use weighted average..
Amount of x/ TOTAL= $$\frac{8-7.6}{8-7}=\frac{0.4}{1}=\frac{2}{5}$$
C
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Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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18 Jul 2017, 02:32
chetan2u

How do you find X and Y? Can you explain?
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Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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18 Jul 2017, 02:44
theharvardafricaner wrote:
chetan2u

How do you find X and Y? Can you explain?

Line up the values in increasing order, with average value in the middle: $$7, 7.6, 8.$$

Now the ratio of $$\frac{X}{Y} = \frac{8 - 7.6}{7.6 - 7} = \frac{0.4}{0.6} = \frac{2}{3}$$.

The question asks for ratio of $$\frac{X}{Total} = \frac{2}{2+3} = \frac{2}{5}.$$
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Posts: 64216
Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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24 Dec 2018, 03:48
Bunuel wrote:

Fresh GMAT Club Tests' Question:

Quentin put an amount of money into each of two new investments, X and Y. Investment X pays x% simple annual interest and investment Y pays y% simple annual interest. After 1 year, the average (arithmetic mean) interest earned by investments X and Y was 7.6%. If x and y are consecutive positive integers, in that order, what fraction of the total amount was put in investment X?

A. 1/5
B. 1/3
C. 2/5
D. 3/5
E. 2/3

_________________
Re: Quentin put an amount of money into each of two new investments, X and   [#permalink] 24 Dec 2018, 03:48