2021 AMC 12B Spring Problem 1

Attempt Problem 1 of the 2021 AMC 12B Spring 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 12B Spring solutions, or check the answer key.

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

1.

How many integer values of xx satisfy ∣x∣<3π?|x| \lt 3\pi?
99
1010
1818
1919
2020
Answer: D
Concepts:absolute valueestimation
Small hint:
3π3\pi is a little more than 99
Big hint:
Count the integers from −9-9 to 99 inclusive
Solution:
Since 3π≈9.42,3\pi \approx 9.42, the inequality ∣x∣<3π|x| \lt 3\pi means −9.42<x<9.42.-9.42 \lt x \lt 9.42.
The integers in this range run from −9-9 to 9,9, giving 1919 values.
Thus, the correct answer is D.
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