2017 AMC 8 Problem 23
Attempt Problem 23 of the 2017 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 2017 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?
Answer: C
Small hint:
Each day’s minutes per mile must divide .
Big hint:
List the divisors of and find four of them spaced apart.
Video solution:
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Written solution:
Linda traveled for minutes every day. Since one mile was traveled in an integer amount of minutes each day, her minutes per mile every day must be a factor of The factors of are and The only sequence of four of these numbers that differ by are and For the four days, she traveled miles in total.
Thus, C is the correct answer.
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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- 2012 AMC 8
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