Question

Andy and Bethany have a rectangular array of numbers with $40$ rows and $75$ columns. Andy adds the numbers in each row. The average of his $40$ sums is $A.$ Bethany adds the numbers in each column. The average of her $75$ sums is $B.$ What is the value of $\dfrac{A}{B}?$

$\dfrac{64}{225}$

$\dfrac{8}{15}$

$1$

$\dfrac{15}{8}$

$\dfrac{225}{64}$

Solution:

Let $S$ be the sum of all numbers in the array.

Andy's $40$ row sums also add to $S$ , so their average is $A=\dfrac{S}{40}$ . Bethany's $75$ column sums also add to $S$ , so their average is $B=\dfrac{S}{75}$ .

Therefore $\dfrac{A}{B}=\dfrac{S/40}{S/75}=\dfrac{75}{40}=\dfrac{15}{8}$ .

Thus, D is the correct answer.

2009 AMC 8 Problem 21

Solution:

Problem 21 in Other Years