2017 AMC 10B Problems/Problem 1
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[hide]Problem
Mary thought of a positive two-digit number. She multiplied it by and added . Then she switched the digits of the result, obtaining a number between and , inclusive. What was Mary's number?
Solution 1
Just try out the answer choices. Multiplying by and then adding and reversing the digits gives you , which works, so the answer is
Solution 2
Working backwards, we reverse the digits of each number from ~ and subtract from each, so we have The only numbers from this list that are divisible by are and . We divide both by , yielding and . Since is not among the answer choices, the correct answer would be
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
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Followed by Problem 2 | |
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