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Difficult OG word prob

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Difficult OG word prob

by gmatblood » Mon Oct 31, 2011 9:25 am
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

A. 1/(r+2)
B. 1(2r+2)
C. 1/(3r+2)
D. 1/(r+3)
E. 1/(2r+3)
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by GmatMathPro » Mon Oct 31, 2011 9:41 am
Let x=the fraction that Henry saves
1-x=fraction that henry spends
T=total income

amount he saves=Tx
amount he will have available to spend next year=Tx(1+r)
amount he spends this year=T(1-x)

We want the amount he has available to spend to be equal to half the amount he spends this year, so:

Tx(1+r)=(1/2)T(1-x)

divide out the T from both sides:

x(1+r)=(1/2)(1-x)

multiply both sides by 2 to get rid of fractions:

2x(1+r)=1-x

2x+2xr=1-x

3x+2xr=1

x(3+2r)=1

x=1/(3+2r)

Ans: E
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by shankar.ashwin » Mon Oct 31, 2011 9:42 am
Assuming values could be faster IMO.
Let income be $100 and saving be $10.
Therefore, he has spend $90 this year and will have $45 the next.

10(1+r)=45
r=3.5. Now substitute this in answer choices to see which one yields our saving amount ($10) this year.
E works. 100/(2*3.5 + 3) = $10
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by GMATGuruNY » Mon Oct 31, 2011 9:56 am
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