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2013 AMC 10A Question 17

AMC10 · 2013 AMC 10A

Question 17

Daphne is visited periodically by her three best friends: Alice, Beatrix, and Claire. Alice visits every third day, Beatrix visits every fourth day, and Claire visits every fifth day.

All three friends visited Daphne yesterday. How many days of the next $365$-day period will exactly two friends visit her?
  1. $48$
  2. $54$
  3. $60$
  4. $66$
  5. $72$