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A showroom is open on all seven days of the week throughout the year. There are five employees Alex, Bhabha, Cathy, Dilip and Ethan who work in the showroom. Every day except Sunday, two employees…

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A showroom is open on all seven days of the week throughout the year. There are five employees Alex, Bhabha, Cathy, Dilip and Ethan who work in the showroom. Every day except Sunday, two employees are required while on Sunday three employees need to work. Every employee works for three days in a week. Some additional information is also provided:

- Every employee works on two consecutive days while the third day is not consecutive to either of them. (The week is continuous, so Sunday and the following Monday count as consecutive days.)
- Alex and Dilip work together on Tuesday and Wednesday while the other working day differs for them.
- Neither Bhabha nor Cathy works with Alex on any day.
- Cathy does not work either on Saturday or on Monday.

One of the days Alex works on is
  1. Monday
  2. Friday
  3. Sunday
  4. Saturday

Answer and explanation

Correct answer: D - Saturday
Alex works Tue, Wed and Saturday. Schedule (unique when Sunday-Monday counts as consecutive): Mon B,E; Tue A,D; Wed A,D; Thu B,C; Fri C,E; Sat A,E; Sun B,C,D. Cathy cannot work Mon/Sat, nor Tue/Wed (Alex), so she takes Thu-Fri and Sun; Alex's third day avoids Cathy's days and Mon (would join Tue-Wed run), so Sat; Mon must be B and E; Sat's partner is E; E on Sun would make Sat-Sun-Mon a three-day run, so Sun = B,C,D; E pairs Fri with Sat and B takes Thu.

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