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by GmatKiss » Fri May 25, 2012 2:44 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) 1/2(r+2)
(C) 1/(3r+2)
(D) 1/(r+3)
(E) 1/(2r+3)
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by Anurag@Gurome » Fri May 25, 2012 2:45 am
GmatKiss wrote: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) 1/2(r+2)
(C) 1/(3r+2)
(D) 1/(r+3)
(E) 1/(2r+3)
Algebraic Approach: Let Henry spends $x and he saves $y. This implies total income = $(x + y)
Then, next year Henry spends $y(1 + r) = x/2 implies x = 2y(1 + r)

We have to find y/(x + y) = y/[2y(1 + r) + y] = y/(3y + 2yr) = 1/(3 + 2r)

The correct answer is E.
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by ronnie1985 » Fri May 25, 2012 10:44 am
x be the fraction he saves then 1-x is the fraction he spends

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

x = 1/(2+3r)
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by GMATGuruNY » Fri May 25, 2012 5:11 pm
I posted an alternate solution here:

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by Brent@GMATPrepNow » Fri May 25, 2012 5:32 pm
GmatKiss wrote: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) 1/2(r+2)
(C) 1/(3r+2)
(D) 1/(r+3)
(E) 1/(2r+3)
Here's an algebraic solution:
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by Brent@GMATPrepNow » Fri May 25, 2012 5:33 pm
GmatKiss wrote: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) 1/2(r+2)
(C) 1/(3r+2)
(D) 1/(r+3)
(E) 1/(2r+3)
Here's a "non-algebraic" solution:
Image

Cheers,
Brent
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