1999 AMC 8 Problem 6
Attempt Problem 6 of the 1999 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 1999 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
6.
Bo, Coe, Flo, Jo, and Moe have different amounts of money. Neither Jo nor Bo has as much money as Flo. Both Bo and Coe have more than Moe. Jo has more than Moe, but less than Bo. Who has the least amount of money?
Bo
Coe
Flo
Jo
Moe
Answer: E
Small hint:
Eliminate anyone known to have more than someone else
Big hint:
Use each comparison to show who is above Moe
Solution:
Let and represent the amount of money that Bo, Coe, Flo, Jo, and Moe have respectively.
Then
We also have
Finally, we are given
From the first and second inequalities, we can get that
This shows that everyone has more money than Moe.
Thus, E is the correct answer.
Problem 6 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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