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2011 AMC 10B Problem 5

Problem 5 of 25EasierNumber Theory

In multiplying two positive integers aa and b,b, Ron reversed the digits of the two-digit number a.a. His erroneous product was 161.161. What is the correct value of the product of aa and b?b?

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Solution

The number 161161 is equal to 7⋅23.7\cdot 23. There are no other pairs of numbers that multiply to 161161 besides 1⋅161,1\cdot 161, so 2323 is the only two digit factor. Thus, 2323 is the number reversed, so he meant to get 32⋅732\cdot 7 which is 224.224. Thus, the correct answer is E .

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Concepts: digits · prime factorization

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.