2021 AMC 12B Spring Problem 1 — Solution | LIVE by Po-Shen Loh

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2021 AMC 12B Spring Problem 1

Below is the professionally curated solution for Problem 1 of the 2021 AMC 12B Spring, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12B Spring solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:absolute value estimation

Difficulty rating: 870

1.

How many integer values of $x$ satisfy $|x| \lt 3\pi?$

$9$

$10$

$18$

$19$

$20$

Solution:

Since $3\pi \approx 9.42,$ the inequality $|x| \lt 3\pi$ means $-9.42 \lt x \lt 9.42.$

The integers in this range run from $-9$ to $9,$ giving $19$ values.

Thus, the correct answer is D.

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