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2015 AMC 12B Problem 6

Problem 6 of 25EasierNumber TheoryCombinatorics

Back in 1930,1930, Tillie had to memorize her multiplication facts from 0×00 \times 0 through 12×12.12 \times 12. 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?

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Solution

The body has 13×13=16913 \times 13 = 169 entries. A product is odd exactly when both factors are odd. There are 66 odd numbers among 0,1,…,12,0, 1, \ldots, 12, giving 6×6=366 \times 6 = 36 odd entries. The fraction is 36169=0.213…≈0.21.\dfrac{36}{169} = 0.213\ldots \approx 0.21. Thus, the correct answer is A.
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Tagged: parity · basic counting

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