2009 AMC 8 Problem 21
Attempt Problem 21 of the 2009 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 2009 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
Andy and Bethany have a rectangular array of numbers with rows and columns. Andy adds the numbers in each row. The average of his sums is Bethany adds the numbers in each column. The average of her sums is What is the value of
Answer: D
Small hint:
Let be the sum of all entries in the array.
Big hint:
Andy has average row sum while Bethany has average column sum
Solution:
Let be the sum of all numbers in the array.
Andy’s row sums also add to so their average is Bethany’s column sums also add to so their average is
Therefore
Thus, D is the correct answer.
Problem 21 in other years
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