2017 AMC 12A Problem 2

Attempt Problem 2 of the 2017 AMC 12A 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 2017 AMC 12A solutions, or check the answer key.

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

The sum of two nonzero real numbers is

4

times their product. What is the sum of the reciprocals of the two numbers?

1

2

4

8

12

The sum of reciprocals is

\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{x+y}{xy}

Divide the equation

x+y=4xy

xy

Let the numbers be

x

and

y,

x+y=4xy.

Dividing both sides by

xy

gives

\dfrac{x+y}{xy}=4,

and the left side is exactly

\dfrac{1}{y}+\dfrac{1}{x}.

So the sum of the reciprocals is

4.

Thus, the correct answer is C.

Problem 2 in other years