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%.

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

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

Users browsing this forum: No registered users and 2 guests

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.