Skip to main content
OlympiadHQ

Browse · harp

Print

smc

number theory senior

Problem

Back in 1930, Tillie had to memorize her multiplication facts from to . The multiplication table she was given had rows and columns labeled with the factors, and the products formed the body of the table. To the nearest hundredth, what fraction of the numbers in the body of the table are odd?
(A)
(B)
(C)
(D)
Solution
There are a total of products, and a product is odd if and only if both its factors are odd. There are odd numbers between and , namely hence the number of odd products is . Therefore the answer is .
Final answer
A