1997 AMC 8 Problem 16
Attempt Problem 16 of the 1997 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
Penni Precisely buys worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up BB was down and CC was unchanged. For the second year, AA was down from the previous year, BB was up from the previous year, and CC was unchanged. If and are the final values of the stock, then
Answer: E
Small hint:
A percent gain followed by a percent loss does not return to the start
Big hint:
Apply each percent change multiplicatively
Solution:
After the first year, AA’s stock’s worth goes up to and BB’s goes down to
After the second year, AA’s stock is worth and BB’s is worth
CC’s stock worth remains the same, so the ordering of the stock worths is now
Thus, E is the correct answer.
Problem 16 in other years
- 1985 AMC 8
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