2015 AMC 10B Problem 6
Attempt Problem 6 of the 2015 AMC 10B 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 2015 AMC 10B solutions, or check the answer key.
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6.
Marley practices exactly one sport each day of the week. She runs three days a week but never on two consecutive days. On Monday she plays basketball and two days later golf. She swims and plays tennis, but she never plays tennis the day after running or swimming. Which day of the week does Marley swim?
Sunday
Tuesday
Thursday
Friday
Saturday
Answer: E
Solution:
Marley plays basketball on Monday and golf on Wednesday. She cannot fit all three running days among Thursday, Friday, Saturday, and Sunday without having two consecutive running days, so Tuesday must be a running day.
From Thursday through Sunday, she must run twice, swim once, and play tennis once. Tennis cannot be the day after running or swimming, so tennis must be Thursday. Then the two remaining running days must be Friday and Sunday, leaving Saturday for swimming.
Thus, the correct answer is E.
Problem 6 in Other Years
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