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Rishi spends $1054.69 on rent each month and receives a set monthly

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Tuck School Moderator
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Rishi spends $1054.69 on rent each month and receives a set monthly  [#permalink]

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New post 20 Aug 2018, 18:36
1
4
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (02:00) correct 33% (02:30) wrong based on 84 sessions

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Rishi spends $1054.69 on rent each month and receives a set monthly income. In January, he saved a certain amount, and for each following month, he saved \(\frac{3}{2}\)as much as the previous month, spending all his remaining income. How much had he saved by the end of the year?

(1) In August, if his rent were $54.69 less and he had saved $8.80 less, his rent and the amount he saved would have been the same.

(2) Each year, his rent is \(\frac{12}{5}\) of his savings.

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Re: Rishi spends $1054.69 on rent each month and receives a set monthly  [#permalink]

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New post 20 Aug 2018, 21:24
Can someone explain how Statement 1 is sufficient?
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Re: Rishi spends $1054.69 on rent each month and receives a set monthly  [#permalink]

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New post 20 Aug 2018, 21:47
(1) find amount saved in August from the clue
And amount for other months given 3/2 and reciprocal
(2) 5/12 times rent is savings
Answer D
Not difficult
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Rishi spends $1054.69 on rent each month and receives a set monthly  [#permalink]

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New post 21 Aug 2018, 07:17
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PeepalTree wrote:
Rishi spends $1054.69 on rent each month and receives a set monthly income. In January, he saved a certain amount, and for each following month, he saved \(\frac{3}{2}\)as much as the previous month, spending all his remaining income. How much had he saved by the end of the year?

(1) In August, if his rent were $54.69 less and he had saved $8.80 less, his rent and the amount he saved would have been the same.

(2) Each year, his rent is \(\frac{12}{5}\) of his savings.


Rent R=1054.69
Income -A
Saving - S
Next month saving is \(\frac{3}{2}S\)....
Our Ans is \(S+(\frac{3}{2})S+S(\frac{3}{2})^2+.......+S(\frac{3}{2})^{11}\)
So we require to know S


(1) In August, if his rent were $54.69 less and he had saved $8.80 less, his rent and the amount he saved would have been the same.
In August his actual saving =\(S(\frac{3}{2})^6\)
New case - rent \(= 1054.69-54.69= 1000\), income = A, And Saving= \(S(\frac{3}{2})^6-8.80\)...
\(S(\frac{3}{2})^6-8.80=1000......S(\frac{3}{2})^6=1008.8\)..
You can get S from this
Sufficient

(2) Each year, his rent is \(\frac{12}{5}\) of his savings
Rent =\(1054.69 *12\)
So \(S*\frac{12}{5} = 1054.69*12.....S=1054.69*5\)
Sufficient

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Rishi spends $1054.69 on rent each month and receives a set monthly   [#permalink] 21 Aug 2018, 07:17
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