2001 AMC 10 Problem 2

Attempt Problem 2 of the 2001 AMC 10 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 2001 AMC 10 solutions, or check the answer key.

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

A number

x

2

more than the product of its reciprocal and its additive inverse. In which interval does the number lie?

-4 \le x \le -2

-2 \lt x \le 0

0 \lt x \le 2

2 \lt x \le 4

4 \lt x \le 6

The reciprocal of

x

\dfrac1x

and the additive inverse is

-x

Their product is

\dfrac1x\cdot(-x)=-1

The reciprocal of

x

\dfrac1x

and its additive inverse is

-x.

Their product is

\dfrac1x\cdot(-x)=-1.

x=2+(-1)=1,

which lies in the interval

0\lt x\le2.

Thus, the correct answer is C.

Problem 2 in other years