1995 AMC 8 Problem 7

Attempt Problem 7 of the 1995 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 1995 AMC 8 solutions, or check the answer key.

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

7.

At Clover View Junior High, one half of the students go home on the school bus. One fourth go home by automobile. One tenth go home on their bicycles. The rest walk home. What fractional part of the students walk home?
116\dfrac{1}{16}
320\dfrac{3}{20}
13\dfrac13
1720\dfrac{17}{20}
910\dfrac{9}{10}
Answer: B
Concepts:fraction
Small hint:
Give the fractions a common denominator to add them
Big hint:
Subtract the total who ride from 11 (the whole group)
Solution:
The students who ride make up
12+14+110=1020+520+220=1720. \begin{aligned} \dfrac12 + \dfrac14 + \dfrac{1}{10} &= \dfrac{10}{20} + \dfrac{5}{20} + \dfrac{2}{20} \\ &= \dfrac{17}{20}. \end{aligned}
So the fraction who walk is 1−1720=320.1 - \dfrac{17}{20} = \dfrac{3}{20}.
Thus, the correct answer is B .
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