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 Post subject: GMAT PercentagePosted: Wed Jan 05, 2011 3:04 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25%
B. 40%
C. 50%
D. 75%
E. 96%

(C) Let’s denote by x amount of money each of them had in savings at the beginning of last year.

Considering changes in Mike’s savings he currently has 1.2 × 0.8 × x = 0.96x
Considering changes in John’s savings he currently has 0.8 × 1.2 × x = 0.96x

In order to calculate what percentage of John’s and Mike’s savings combined are John’s savings alone we divide Jon’s savings alone by John’s and Mike’s savings combined:
0.96x / (0.96x + 0.96 x) = 1/2 =0.5 = 50%.

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In this question, the assumption is that the decrease/increase in savings in the begening of this year were on the original saving amount. Why is it so?

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 Post subject: Re: GMAT PercentagePosted: Wed Jan 05, 2011 3:19 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
There is NO such assumption. In the explanation we apply increase/decrease simultaneously. Let's consider it in steps.

Let’s denote by x amount of money each of them had in savings at the beginning of last year.
Mike’s savings by the end of last year increased by 20%: 1.2x
John’s savings by the end of last year decreased by 20%: 0.8x

Mike’s savings decreased by 20% this year: (1.2x) × 0.8 = 0.96x
John's savings increased by 20% this year: (0.8x) × 1.2 = 0.96x

The rest of the reasoning is the same.

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