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All, this Q has been discussed many times. I'm interested in

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All, this Q has been discussed many times. I'm interested in [#permalink] New post 24 Mar 2008, 02:00
All, this Q has been discussed many times. I'm interested in plugging numbers approach since solving this Q can result in arithmetic errors. Any takers?
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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Re: set27 Q19 - Henry [#permalink] New post 24 Mar 2008, 03:02
GGUY wrote:
All, this Q has been discussed many times. I'm interested in plugging numbers approach since solving this Q can result in arithmetic errors. Any takers?
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)


Well, in my opinion, it's not that hard to just solve in a direct way

Let T=total amount he earns in first year
A = proportion he saves (and this is what we wanna find)

Thus, amount he saves in first year = TA
amount he spends = T(1-A)
in second year, amount he saves will become TA(1+r)

we get equation TA(1+r) = T(1-A)/2
2TA(1+r) = T(1-A)
2A(1+r) = 1-A
2A+2Ar = 1-A
3A+2Ar = 1
A(3+2r) = 1
A = 1/(3+2r)
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Re: set27 Q19 - Henry [#permalink] New post 24 Mar 2008, 07:02
prov wrote:
GGUY wrote:
All, this Q has been discussed many times. I'm interested in plugging numbers approach since solving this Q can result in arithmetic errors. Any takers?
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)


Well, in my opinion, it's not that hard to just solve in a direct way

Let T=total amount he earns in first year
A = proportion he saves (and this is what we wanna find)

Thus, amount he saves in first year = TA
amount he spends = T(1-A)
in second year, amount he saves will become TA(1+r)

we get equation TA(1+r) = T(1-A)/2
2TA(1+r) = T(1-A)
2A(1+r) = 1-A
2A+2Ar = 1-A
3A+2Ar = 1
A(3+2r) = 1
A = 1/(3+2r)


I echo what prov said... inafct chosing values will take longer because of the math involved with r and divisions. Solving it directly is not very hard and guess is the quickest way.
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Re: set27 Q19 - Henry [#permalink] New post 27 Sep 2008, 05:16
the equation is- (R-C)*(1+r)=C, where R=Revenue, C=consume, S= savings

=> (R-C)/C = 1/(1+r)

=> R/C = (2+r)/)1+r)

=> C/R = (1+r)/(2+r)

=> S/R = 1-C/R = 1-(1+r)/(2+r) = 1/(2+r)

thus A
Re: set27 Q19 - Henry   [#permalink] 27 Sep 2008, 05:16
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