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person will save a certain amnt of income this yr and spend

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Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
GMAT 2: 660 Q V
GPA: 3.64
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 46 [0], given: 72056

person will save a certain amnt of income this yr and spend [#permalink] New post 08 Sep 2004, 11:07
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C
D
E

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  5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
person will save a certain amnt of income this yr and spend the rest. next yr person will have no income but for each $ saved this yr, will have 1+r next year. in terms of r wht fraction of the income shud person save so that next year amnt avilable to spend is half the amount spent this year

1. 1/(r+2)
2. 1/(2r+2)
c. 1/(3r+2)
d. 1/(r+3)
e. 1/(2r+3)

please explain
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Joined: 05 Sep 2004
Posts: 97
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 [#permalink] New post 08 Sep 2004, 12:29
Okie dokie.

Let:

I = Total income earned this year
C = Total amount consumed this year
S = Total amount saved this year

i.e., I = C + S

Now, the question imposes the following condition:

Amount available to spend next year = Half the amount spent this year = C/2

Where:
Amount available to spend next year = Amount saved this year * (1+r) = S(1+r)

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

Substituting in our income formula above:

I = 2S(1+r) + S = S[1+2(1+r)] = S(2r+3)
=> S/I = 1/(2r+3) = Portion of I saved this year.

Answer is E.
Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
GMAT 2: 660 Q V
GPA: 3.64
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 46 [0], given: 72056

 [#permalink] New post 08 Sep 2004, 12:47
Perfect Intr3pid. Got the same, used, X (income) and Y (expense for this year = X-$, where $=saving this year) instead. The catch is to read this properly..

For every $ saved this year, the person will have (1+r) next year. Which is $(1+r) = (X-$)/2

=>2$+2r$=X-$
=>3$+2r$=X
=>$(3+2r)=X

Question is X/$=? and we have from above = 1/(3+2r).
E.
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 [#permalink] New post 08 Sep 2004, 12:51
sorry, guest was me...as always forgot to login.
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 [#permalink] New post 08 Sep 2004, 18:33
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 [#permalink] New post 08 Sep 2004, 18:52
Assume person earns $y and save $x, so he spends $y-x
Next year, he wil have $(1+r)x

Amt availble x+rx = y - x
2x+rx = y
x(2+r) = y
x/y = 1/(2+r)

x/y = faction of income that needs to be saved
  [#permalink] 08 Sep 2004, 18:52
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person will save a certain amnt of income this yr and spend

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