1994 AMC 8 Problem 13

Attempt Problem 13 of the 1994 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 1994 AMC 8 solutions, or check the answer key.

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

13.

The number halfway between 16\dfrac{1}{6} and 14\dfrac{1}{4} is
110\dfrac{1}{10}
15\dfrac{1}{5}
524\dfrac{5}{24}
724\dfrac{7}{24}
512\dfrac{5}{12}
Answer: C
Concepts:meanfraction
Small hint:
The number halfway between two numbers is their average
Big hint:
Add 16\dfrac16 and 14,\dfrac14, then divide the sum by 22
Solution:
The number halfway between two values is their average: 16+142.\dfrac{\frac16 + \frac14}{2}.
Since 16+14=212+312=512,\dfrac16 + \dfrac14 = \dfrac{2}{12} + \dfrac{3}{12} = \dfrac{5}{12}, the average is 512÷2=524.\dfrac{5}{12} \div 2 = \dfrac{5}{24}.
Thus, the correct answer is C .
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