2006 AMC 8 Problem 22
Attempt Problem 22 of the 2006 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 2006 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cell?
Answer: D
Small hint:
Write the three bottom entries as and .
Big hint:
The middle bottom entry is counted twice in the top number.
Solution:
If the lower cells contain and the middle row will have and .
This means that the top row will have . To minimize this, put in the middle and and in the outer cells. This yields a top number of .
To maximize it, put in the middle and and in the outer cells. This yields a top number of . The desired difference is .
Thus, D is the correct answer.
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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