1958 AMC 12 Problem 13

Attempt Problem 13 of the 1958 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 1958 AMC 12 solutions, or check the answer key.

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

13.

The sum of two numbers is

10;

their product is

20.

The sum of their reciprocals is:

\dfrac1{10}

\dfrac12

1

2

4

Call the numbers

x

and

y

, but do not solve for them individually

Use

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

If the numbers are

x

and

y,

then

\frac1x+\frac1y =\frac{x+y}{xy} =\frac{10}{20} =\frac12.

Therefore, the correct answer is B.

Problem 13 in other years