1993 AMC 8 Problem 16

Attempt Problem 16 of the 1993 AMC 8 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 1993 AMC 8 solutions, or check the answer key.

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

16.

What is the value of the following expression?
11+12+13\cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{3}}}
16\dfrac16
310\dfrac{3}{10}
710\dfrac{7}{10}
56\dfrac56
103\dfrac{10}{3}
Answer: C
Concepts:continued fractionfraction
Small hint:
Work from the bottom up: first simplify 2+132 + \dfrac13
Big hint:
Then 1+173=1+37,1 + \dfrac{1}{\frac{7}{3}} = 1 + \dfrac37, and take the reciprocal
Solution:
Starting inside, 2+13=73,2 + \dfrac13 = \dfrac73, so 173=37.\dfrac{1}{\frac{7}{3}} = \dfrac37.
Then 1+37=107,1 + \dfrac37 = \dfrac{10}{7}, and the whole expression is 1107=710.\dfrac{1}{\frac{10}{7}} = \dfrac{7}{10}.
Thus, the correct answer is C .
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