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

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Director
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This year Henry will save a certain amount of his income, [#permalink] New post 29 Apr 2006, 21:03
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A
B
C
D
E

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0% (00:00) correct 0% (00:00) wrong based on 1 sessions
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)
Manager
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 [#permalink] New post 30 Apr 2006, 06:15
:oops: I dunno how to do this one. Whoever cracks it, please explain it.
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 [#permalink] New post 30 Apr 2006, 08:14
It looks like D.....

I will explain if D is correct...Thanks ... :wink:
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 [#permalink] New post 30 Apr 2006, 08:44
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)

Add 1 to both sides
y/(x-y) + 1 = 2(1+r) + 1
x/(x-y) = 2r+3

Hence (x-y)/x = 1/(2r+3)
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 [#permalink] New post 30 Apr 2006, 08:50
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)

Add 1 to both sides
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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 [#permalink] New post 30 Apr 2006, 11:02
Thanks Giddi,

I don't think this would have struck me had I seen it on the test :?
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 [#permalink] New post 01 May 2006, 00:39
OA is 'E'.

Perfect Giddi. :-D
  [#permalink] 01 May 2006, 00:39
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