1991 AMC 12 Problem 3

Attempt Problem 3 of the 1991 AMC 12 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 1991 AMC 12 solutions, or check the answer key.

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

\left(4^{-1}-3^{-1}\right)^{-1}=

-12

-1

\frac1{12}

1

12

Rewrite the negative first powers as reciprocals

First simplify

\frac14-\frac13

, then take its reciprocal

We have

4^{-1}-3^{-1}=\frac14-\frac13=-\frac1{12}.

Raising this result to the power

-1

takes its reciprocal, giving

-12.

Thus the correct answer is A.

Problem 3 in other years