Question

Three-digit powers of $2$ and $5$ are used in this ''cross-number'' puzzle. What is the only possible digit for the outlined square? $\begin{array}{lcl} \boldsymbol{\rightarrow} & & \boldsymbol{\downarrow} \\ \textbf{2. } 2^m & & \textbf{1. } 5^n \end{array}$

$0$

$2$

$4$

$6$

$8$

Answer: D

Concepts:digits systematic listing

Difficulty rating: 1020

Solution:

The only $3$ -digit powers of $5$ are $125$ and $625.$ This means that the $2$ spot is filled with a $2.$

The only $3$ -digit power of $2$ beginning with a $2$ is $256,$ so the outlined square is filled with a $6.$

Thus, D is the correct answer.

2000 AMC 8 Problem 9

Answer: D

Difficulty rating: 1020

Solution:

Problem 9 in Other Years