2017 AMC 10B Problem 1

Attempt Problem 1 of the 2017 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2017 AMC 10B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

$11$

$12$

$13$

$14$

$15$

Answer: B

Concepts:digits divisibility work backwards

Difficulty rating: 960

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 .

Full Exam

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