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# This year Henry will save a certain amount of his income,

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Senior Manager
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This year Henry will save a certain amount of his income, [#permalink]

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29 Apr 2006, 22:03
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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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30 Apr 2006, 07:15
I dunno how to do this one. Whoever cracks it, please explain it.
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30 Apr 2006, 09:14
It looks like D.....

I will explain if D is correct...Thanks ...
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30 Apr 2006, 09:44
Should be E.

x = This year's income
y = this year's spending
x-y = this year's saving

Next year's amount avaulable for spending = (x-y)(1+r)
Required (x-y)/x ?

Given:
(x-y)(1+r) = y/2

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

y/(x-y) + 1 = 2(1+r) + 1
x/(x-y) = 2r+3

Hence (x-y)/x = 1/(2r+3)
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30 Apr 2006, 09:50
giddi77 wrote:
Should be E.

x = This year's income
y = this year's spending
x-y = this year's saving

Next year's amount avaulable for spending = (x-y)(1+r)
Required (x-y)/x ?

Given:
(x-y)(1+r) = y/2

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

y/(x-y) + 1 = 2(1+r) + 1
x/(x-y) = 2r+3

Hence (x-y)/x = 1/(2r+3)

Good solution with a lot of clarity.....Thanks!!
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30 Apr 2006, 12:02
Thanks Giddi,

I don't think this would have struck me had I seen it on the test
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01 May 2006, 01:39
OA is 'E'.

Perfect Giddi.
01 May 2006, 01:39
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