2013 AMC 8 Problem 21
Attempt Problem 21 of the 2013 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
Samantha lives blocks west and block south of the southwest corner of City Park.
Her school is blocks east and blocks north of the northeast corner of City Park. On school days she bikes on streets to the southwest corner of City Park, then takes a diagonal path through the park to the northeast corner, and then bikes on streets to school.
If her route is as short as possible, how many different routes can she take?
Answer: E
Small hint:
Count shortest street routes before and after the park separately.
Big hint:
There are ways before the park and ways after it.
Video solution:
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Written solution:
To reach the southwest corner of the park as quickly as possible, Samantha must go blocks east and block north, which can be arranged in ways. After the diagonal path through the park, she must go blocks east and blocks north to reach school, which can be arranged in ways.
The choices before and after the park are independent, so the total number of shortest routes is .
Thus, E is the correct answer.
Problem 21 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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