2000 AMC 8 Problem 2 — Solution | LIVE by Po-Shen Loh

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2000 AMC 8 Problem 2

Attempt Problem 2 of the 2000 AMC 8 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 2000 AMC 8 solutions, or check the answer key.

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

2.

Which of these numbers is less than its reciprocal?

$-2$

$-1$

$0$

$1$

$2$

Answer: A

Concepts:inequality

Difficulty rating: 450

Solution:

$0$ has no reciprocal, and $1$ and $-1$ are their own reciprocals.

The reciprocal of $2$ is $\frac{1}{2},$ but $2$ is not less than $\frac{1}{2}.$

Therefore, as $-2 < -\frac 12,$ we know that $-2$ is the only one of the answer choices that is less than its reciprocal.

Thus, A is the correct answer.

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