2020 AMC 8 Problem 16
Attempt Problem 16 of the 2020 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
Each of the points and in the figure below represents a different digit from to Each of the five lines shown passes through some of these points. The digits along each line are added to produce five sums, one for each line. The total of the five sums is What is the digit represented by
Answer: E
Small hint:
Most points are counted twice in the five line sums
Big hint:
Point is counted one extra time
Video solution:
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Written solution:
Every point is counted in two of the line sums except which is counted in three. Thus the total of the five line sums is twice the sum of all six digits, plus one extra
The digits are exactly and whose sum is Therefore so
Thus, the correct answer is E.
Problem 16 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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