The value of a share was 25% less in the 2nd quarter over

BTGmoderatorLU wrote:Source: e-GMAT

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%

Let's assign a nice value to the share value in the 1st quarter.

Let's say the share value in the 1st quarter = $100

The value of a share was 25% less in the 2nd quarter over the 1st quarter . . .
So, the share value in the 2nd quarter = $100 - (25% of $100)
= $100 - $25
= $75

. . . and 20% more in the 3rd quarter over the 2nd quarter.
So, the share value in the 3rd quarter = $75 + (20% of $75)
= $75 + $15
= $90

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%?
Let's first examine what it means for the percentage increase of the value from 1st to 4th quarter to be 20%
So 20% of $100 = $20
So, a 20% increase from 1st to 4th quarter means the 4th quarter value = $100 + $20 = $120

So, we want the share price to increase from $90 (3rd quarter price) to $120 (4th quarter price)
Percent change = 100(new - old)/old
= 100($120 - 90)/90
= 100(30)/(90)
= 100(1)/(3)
= 33 1/3%

Answer: E

Cheers,
Brent

BTGmoderatorLU wrote:Source: e-GMAT

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%

The OA is E.

We can let n = the first quarter value. Therefore, the 2nd quarter value is 0.75n, and the 3rd quarter value is 0.75n x 1.2 = 0.9n.

We need the 4th quarter value to be 1.2n.

So let’s determine what percent increase we need from the 3rd to the 4th quarter.

0.9n * (100 + x)/100 = 1.2n

9(100 + x)/100 = 12

900 + 9x = 1200

9x = 300

x = 33.3

Alternate Solution:

Let’s assume that the value of a share in Q1 was 100. After a 25% decrease, the value in Q2 was (100)(0.75) = 75. Then, in Q3, the share increased by 20%, so its value at the end of Q3 was (75)(1.2) = 90.

The desired value for the share for Q4 is 20% more than its value in Q1, which is (100)(1.2) = 120. We need to determine the percent increase needed from Q3 (90) to Q4(120).

Using the percent increase formula (New - Old)/Old x 100, we have:

(120 - 90)/90 x 100 = 30/90 x 100 = 1/3 x 100 = 33.3%.

Answer: E