2021 Fall AMC 10A Problem 1

Problem 1 of 25EasierAlgebra

What is the value of the following expression?

\dfrac{(2112-2021)^2}{169}

Show solution

Solution

Since

2112-2021=91=7\cdot13,

\begin{aligned} \frac{(2112-2021)^2}{169} &=\frac{(7\cdot13)^2}{13^2}\\ &=7^2=49. \end{aligned}

Thus, C is the correct answer.

Concepts: fraction · exponent

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.