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kaveri_princess
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value of investment

by kaveri_princess Thu Nov 11, 2010 5:40 am

The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ?
200x
________
100 + 2x


x(2 + x)
________
(1 + x)2


2x
_______
1 + 2x


x(200 + x)
_________
10,000


100 -10,000
___________
100 + x
jnelson0612
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Re: value of investment

by jnelson0612 Thu Nov 11, 2010 6:53 pm

kaveri_princess wrote:The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ?
200x
________
100 + 2x


x(2 + x)
________
(1 + x)2


2x
_______
1 + 2x


x(200 + x)
_________
10,000


100 -10,000
___________
100 + x


kaveri,
I think the easiest and best way to handle this problem is to pick numbers. First, let's pick an amount of money to start with. Since we are dealing with percents, let's pick $100.

Now, we need to increase $100 by x% in January and decrease that result by y% in February, and have the amount return back to $100.

I decided to choose x=25. So a 25% increase is $125. Then I need to reduce that amount by $25 to take it back to $100. $25/$125 is 20%, thus y=20.

The question asks "what is y in terms of x"? When you pick numbers, mentally cross off anything about "in terms of (variable)". So the real question is "what is y"? Our answer is 20, so that is what we are targeting.

E is actually the answer, and it needs to be written differently so you can reach your target. It should be:
E) 100 - (10,000/100 + x)
If you substitute x-25, you get:
100 - (10,000/125)
100 - 80 = 20, which matches our target

Thank you,
Jamie Nelson
ManhattanGMAT Instructor
cecammiade
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Re: value of investment

by cecammiade Thu Dec 01, 2011 12:31 am

Are you able to say this?

z= original investment

Month one would be z(1+x) = y

After month two, we know the investment equals the original so

z= z(1+x)(1-y)

simplifying

1=(1+x)(1-y)

1/(1-y)=(1+x)

take the reciprocal

1-y=1/(1+x)

hence

y=1-1/(1+x)

now the format looks very similar to E but isn't quite there.

Any ideas on what I should do now to get the desired end format?
tim
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Re: value of investment

by tim Tue Dec 13, 2011 2:47 am

You’re very close. An increase of x% means you should multiply by (1 + x/100), not just (1+x). Try that and see if you can get the problem to work out..
Tim Sanders
Manhattan GMAT Instructor

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