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

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

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New post 17 Jul 2017, 00:12
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A
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C
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E

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  55% (hard)

Question Stats:

67% (02:42) correct 33% (02:51) wrong based on 65 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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Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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New post 17 Jul 2017, 00:55
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

Therefore, answer is 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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New post 17 Jul 2017, 03:34
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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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New post 17 Jul 2017, 04:08
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= \(\frac{8-7.6}{8-7}=\frac{0.4}{1}=\frac{2}{5}\)
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Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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New post 18 Jul 2017, 03:32
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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New post 18 Jul 2017, 03:44
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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Re: Quentin put an amount of money into each of two new investments, X and  [#permalink]

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New post 24 Dec 2018, 04:48
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


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Re: Quentin put an amount of money into each of two new investments, X and   [#permalink] 24 Dec 2018, 04:48
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