Question

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

$A = B = C$

$A = B \lt C$

$C \lt B = A$

$A \lt B \lt C$

$B \lt A \lt C$

Solution:

After the first year, AA's stock's worth goes up to $\$ 100 \cdot 1.2 = \$ 120$ and BB's goes down to $\$ 100 \cdot .75 = \$ 75.$

After the second year, AA's stock is worth $\$ 120 \cdot .8 = \$ 96$ and BB's is worth $\$ 75 \cdot 1.25 = \$ 93.75.$

CC's stock worth remains the same, so the ordering of the stock worths is now $B \lt A \lt C.$

Thus, E is the correct answer.

1997 AMC 8 Problem 16

Solution:

Problem 16 in Other Years