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

D

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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