2022 AMC 12A Problem 1 — Solution | LIVE by Po-Shen Loh

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2022 AMC 12A Problem 1

Attempt Problem 1 of the 2022 AMC 12A 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 2022 AMC 12A 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

$3+\cfrac{1}{3+\cfrac{1}{3+\frac13}}?$

$\dfrac{31}{10}$

$\dfrac{49}{15}$

$\dfrac{33}{10}$

$\dfrac{109}{33}$

$\dfrac{15}{4}$

Answer: D

Concepts:continued fraction fraction

Difficulty rating: 890

Solution:

Simplify from the bottom. The innermost fraction is $3+\dfrac13=\dfrac{10}{3}.$

The next layer is $3+\dfrac{1}{10/3}=3+\dfrac{3}{10}=\dfrac{33}{10}.$

Finally, $3+\dfrac{1}{33/10}=3+\dfrac{10}{33}=\dfrac{109}{33}.$

Thus, the correct answer is D.

Problem 2#2 →

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