2017 AMC 10B Problem 1

Mary thought of a positive two-digit number. She multiplied it by

3

and added

11.

Then she switched the digits of the result, obtaining a number between

71

and

75,

inclusive. What was Mary’s number?

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Solution

Work backward from the possible results. Reversing

71,72,73,74,75

gives

17,27,37,47,57,

respectively. Subtracting

11

gives

6,16,26,36,46.

Only

6

and

36

are divisible by

3,

and only

36\div3=12

is a two-digit number. Thus, the correct answer is B .

Tagged: digits · divisibility · work backwards