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Henry saves some cash

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DMGLATT
 Post subject: Henry saves some cash
 Post Posted: Mon Apr 21, 2008 11:47 pm 
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 has available to spend will be equal to half the amount that he spends this year?

a) 1/(r+2)
b) 1/(2r+s)
c) 1/(3r+2)
d) 1/(r+3)
e) 1/(2r+3)

This question is from GMAT Focus Test #2

Answer: E - Why oh why?
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RonPurewal
 Post subject:
 Post Posted: Thu Apr 24, 2008 3:53 am 
Offline
ManhattanGMAT Staff


Posts: 7146
this may look like a vic problem at first, but the vic method is extremely difficult to apply to it. it can be done, but you still wind up having to solve an algebra equation; i can show you how it works if you like.

--

so let's just grind it.

let's just say that henry's entire income this year is one dollar, so that 'what fraction of his income' just becomes 'how much'.

thus:
let x = the amount henry saves this year
then 1 - x = the amount he spends
so
next year he will have (1 + r)x dollars to spend = x + rx

the problem tells us that this quantity has to be half of (1 - x).
so
(1 - x)/2 = x + rx

double both sides: 1 - x = 2x + 2rx

segregate terms involving x from those not involving x: 1 = 3x + 2rx

factor out x: 1 = x(3 + 2r)

divide --> answer = e

--

that's a tough problem, man
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700+
 Post subject: Re: Henry saves some cash
 Post Posted: Mon Sep 19, 2011 6:33 am 
Offline
Students


Posts: 23
Location: Bangalore
Got to say..Superb approach!!
This is an Official Guide problem.
OG 12, PS, Question no. 163
The solution you've provided is much better than how its been explained in OG as well as in Manhattan's Official Guide Companion.
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RonPurewal
 Post subject: Re: Henry saves some cash
 Post Posted: Tue Sep 20, 2011 7:40 am 
Offline
ManhattanGMAT Staff


Posts: 7146
linzphilipv wrote:
Got to say..Superb approach!!
This is an Official Guide problem.
OG 12, PS, Question no. 163
The solution you've provided is much better than how its been explained in OG as well as in Manhattan's Official Guide Companion.


thanks, but remember that you shouldn't be concerned with whether one approach is better than another. if you just collect as many approaches as possible, then your situation will be optimal.
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