The value of a share was 25% less in the 2nd quarter over the 1st quarter, and 20% more in the 3rd quarter over the 2nd

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

The value of a share was 25% less in the 2nd quarter over the 1st quarter, and 20% more in the 3rd quarter over the 2nd

by BTGmoderatorDC » Fri May 01, 2020 5:00 pm

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The value of a share was 25% less in the 2nd quarter over the 1st quarter, and 20% more in the 3rd quarter over the 2nd quarter. What should be the percentage change in the value from 3rd to 4th quarter, if the percentage increase of the value from 1st to 4th quarter is 20%?

A. -33.3%
B. -20%
C. 0
D. +20%
E. +33.3%

OA E

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Fri May 01, 2020 5:00 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

Re: The value of a share was 25% less in the 2nd quarter over the 1st quarter, and 20% more in the 3rd quarter over the

by deloitte247 » Sun May 03, 2020 5:06 am

Given that value of a share :
2nd quarter = 25% less than 1st quarter
3rd quarter = 20% more than 2nd quarter
4th quarter = 20% more than 1st quarter

Target question => What should be the percentage change in the value from 3rd to 4th quarter?

Let value of a share in 1st quarter = 100
2nd quarter = 100 * (100% - 25%) = 100 * 75% = 75
3rd quarter = 75 * (100 + 20 %) = 75 * 120% = 90
4th quarter = 100 * (100% + 20%) = 100 * 120% = 120

Between the 3rd and 4th quarter, there is a percentage increase
$$\%\ increase\frac{120\ -\ 90}{90}\cdot\frac{100}{1}=\ \frac{30}{90}\cdot\frac{100}{1}$$
$$\frac{1}{3}\cdot100\ =\ 33.33\%$$
$$Answer\ =\ +33.33\%$$

Answer = E