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2002 AMC 10A Problem 15

Problem 15 of 25IntermediateNumber Theory

The digits 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, 7,7, and 99 are used to form four two-digit prime numbers, with each digit used exactly once. What is the sum of these four primes?

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Solution

A two-digit prime cannot end in 2,2, 4,4, 5,5, or 6,6, so these four are the tens digits and 1,1, 3,3, 7,7, and 99 are the units digits. The sum is 10(2+4+5+6)10(2+4+5+6) +(1+3+7+9)+(1+3+7+9) =170+20=190.=170+20=190. One valid set is {23,47,59,61}.\{23,47,59,61\}. Thus, the correct answer is E.

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Concepts: prime · digits · place value

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