Mathematics
Pink Kangaroo
2023
13

13

We will call a two-digit number power-less if neither of its digits can be written as an integer to a power greater than 1. For example, 53 is power-less, but 54 is not power-less since 4 = 22 . Which of the following is a common divisor of the smallest and the largest power-less numbers?

A 3 B 5 C 7 D 11 E 13

Answer

D

SOLUTIOn

The digits of a power-less number can be only 2, 3, 5, 6, and 7. The smallest two-digit number is 22 and the largest one is 77, and they have a common divisor of 11.

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