Problem:
Penni Precisely buys $100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up 20%, BB was down 25%, and CC was unchanged. For the second year, AA was down 20% from the previous year, BB was up 25% from the previous year, and CC was unchanged. If A,B, and C are the final values of the stock, then
Answer Choices:
A. A=B=C
B. A=B<C
C. C<B=A
D. A<B<C
E. B<A<C
Solution:
At the end of two years, stock values are:
​Stock AA: Stock BB: Stock CC: ​​$100(1.2)(0.8)=$96$100(0.75)(1.25)=$93.75$100(1)(1)=$100​
So, B<A<C.
Answer: E​.
The problems on this page are the property of the MAA's American Mathematics Competitions