2021 AMC 10A Fall Problem 1

Attempt Problem 1 of the 2021 AMC 10A Fall below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10A Fall solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

1.

What is the value of the following expression?

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

7

21

49

64

91

Answer: C

Concepts:fraction exponent

Difficulty rating: 450

Small hint:

2112-2021=91=7\cdot13

Big hint:

The denominator is

13^2

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.