AMC10 2017 B

AMC10 2017 B · Q1

AMC10 2017 B · Q1. It mainly tests Money / coins, Divisibility & factors.

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?

玛丽想了一个两位正整数。她将其乘以3并加11。然后她交换结果的各位数字，得到一个71到75（包含两端）之间的数。玛丽的数是多少？

(A) 11 11

(B) 12 12

(D) 14 14

(E) 15 15

Answer

Correct choice: (B)

正确答案：（B）

Solution

Working backwards, switching the digits of the numbers 71, 72, 73, 74, and 75 and subtracting 11 gives, respectively, 6, 16, 26, 36, and 46. Only 6 and 36 are divisible by 3, and only $36 \div 3 = 12$ is a two-digit number.

逆向工作，对71、72、73、74和75交换各位数字并减11，分别得到6、16、26、36和46。只有6和36能被3整除，且只有$36 \div 3 = 12$是两位数。

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