1993 AMC 8 Problem 16 — Solution | LIVE by Po-Shen Loh

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1993 AMC 8 Problem 16

Below is the professionally curated solution for Problem 16 of the 1993 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1993 AMC 8 solutions, or check the answer key.

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

Concepts:continued fraction fraction

Difficulty rating: 860

16.

What is the value of the following expression?

$\cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{3}}}$

$\dfrac16$

$\dfrac{3}{10}$

$\dfrac{7}{10}$

$\dfrac56$

$\dfrac{10}{3}$

Solution:

Starting inside, $2 + \dfrac13 = \dfrac73,$ so $\dfrac{1}{7/3} = \dfrac37.$

Then $1 + \dfrac37 = \dfrac{10}{7},$ and the whole expression is $\dfrac{1}{10/7} = \dfrac{7}{10}.$

Thus, the correct answer is C .

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