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M16-06

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M16-06  [#permalink]

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New post 16 Sep 2014, 00:58
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  25% (medium)

Question Stats:

83% (01:19) correct 17% (02:09) wrong based on 86 sessions

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Project A requires $2000 of investment and promises a return of \(x\)% per year. Project B requires $3000 of investment and promises a return of \(y\)% per year. If the yearly return from project B is 50% greater than that from project A, what is \(x^2 - y^2\) ?

A. 0
B. 1
C. 5
D. 10
E. 15

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Re M16-06  [#permalink]

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New post 16 Sep 2014, 00:58
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Official Solution:

Project A requires $2000 of investment and promises a return of \(x\)% per year. Project B requires $3000 of investment and promises a return of \(y\)% per year. If the yearly return from project B is 50% greater than that from project A, what is \(x^2 - y^2\) ?

A. 0
B. 1
C. 5
D. 10
E. 15

It follows from the stem that \(2000*\frac{x}{100}*1.5 = 3000*\frac{y}{100}\). From here \(x = y\) and therefore \(x^2 - y^2 = 0\).

Answer: A
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Re: M16-06  [#permalink]

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New post 08 Feb 2017, 22:59
Profit from project B = 30y , Profit from project A = 20x

30y=20x*1.5
=> (x-y) = 0

x^2-y^2 = (x+y) (x-y) = 0
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Re: M16-06  [#permalink]

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New post 13 Jan 2018, 14:46
I am sorry but it is little confusing, Project B give 50 % higher returns than Project A. so Y = 1.5 and X=1. let’s say x= 100% and Y= 150% than how come X^2-Y^2= 0? Apology in advances if I asked very dumb question.
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Re: M16-06  [#permalink]

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New post 13 Jan 2018, 15:48
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sunny012 wrote:
I am sorry but it is little confusing, Project B give 50 % higher returns than Project A. so Y = 1.5 and X=1. let’s say x= 100% and Y= 150% than how come X^2-Y^2= 0? Apology in advances if I asked very dumb question.


The yearly return from project B is 50% greater than that from project A, does not mean that y = 1.5x, it means that the amount earned from project B is 50% greater than that from project A, so \(2000*\frac{x}{100}*1.5 = 3000*\frac{y}{100}\).
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Re: M16-06   [#permalink] 13 Jan 2018, 15:48
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