2021 Fall AMC 12A Problem 1

Problem 1 of 25EasierAlgebra Number Theory

What is the value of

\frac{(2112 - 2021)^2}{169}?

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Solution

Since

2112 - 2021 = 91 = 7 \cdot 13

and

169 = 13^2,

the fraction is

\dfrac{(7 \cdot 13)^2}{13^2} = 7^2 = 49.

Thus, the correct answer is C.

Concepts: factoring · perfect square

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