Bunuel
In January, the value of a stock increased by 25%; and in February, it decreased by 20%. In March, it increased by 50%; and in April, it decreased by 40%. If Jack invested $80 in the stock on January 1 and sold it at the end of April, what was the percentage change in the price of the stock?
(A) 0%
(B) 5%
(C) 10%
(D) 40%
(E) 50%
Since our answer choices are percentages, we do not need to use 80 as the stock price on January 1. We can use variable n. Thus, we have:
n x 5/4 x 4/5 x 15/10 x 6/10
n x 3/2 x 3/5 = 9n/10 = 90n/100 = 0.9n
Thus, we see the percent change is 10%.
Alternate Solution:
Since our answer choices are percentages, we do not need to use 80 as the stock price on January 1. Let’s instead use the more convenient number 100 as the starting price. In January, the stock’s value is 100 x 1.25 = 125. In February, the value is 125 x 0.80 = 100. In March, its value is 100 x 0.5 = 150, and in April it is 150 x 0.6 = 90.
Thus it has dropped $10, from $100 to $90, which is a 10% decrease.
Answer: C