2017 AMC 10A Problem 5

Attempt Problem 5 of the 2017 AMC 10A 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 10A 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

Name the two numbers

x

and

y

Divide the given equation by

xy

Let

x

and

y

be the two numbers. We are given that

x + y = 4xy.

Note that

\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{x + y}{xy} = 4.

Thus, C is the correct answer.

Problem 5 in other years