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# M16-06

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Math Expert
Joined: 02 Sep 2009
Posts: 52442

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15 Sep 2014, 23:58
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

82% (01:17) correct 18% (02:09) wrong based on 84 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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Math Expert
Joined: 02 Sep 2009
Posts: 52442

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15 Sep 2014, 23:58
1
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 $$x^2 - y^2 = 0$$.

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Intern
Joined: 23 Dec 2011
Posts: 34

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08 Feb 2017, 21:59
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
Intern
Joined: 25 Dec 2015
Posts: 4

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13 Jan 2018, 13:46
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.
Math Expert
Joined: 02 Sep 2009
Posts: 52442

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13 Jan 2018, 14:48
1
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 &nbs [#permalink] 13 Jan 2018, 14:48
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# M16-06

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