2017 AMC 10B Problems/Problem 1
Contents
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
We try out each answer choice. Multiplying by , adding , and reversing the digits yields . Therefore 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 a two-digit number, the answer is .
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
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