Question:hard

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

If the Professor conducts a quiz on Tuesday, then her schedule for evaluating quizzes could be:

Show Hint

A quiz on Tuesday fixes the three quiz mornings; use that plus the rule of exactly one evaluation morning to rule out options fast.
Updated On: Jul 10, 2026
  • Monday morning, Monday afternoon, Friday morning, Friday afternoon
  • Monday morning, Friday afternoon, Saturday morning, Saturday afternoon
  • Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon
  • Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon
Show Solution

The Correct Option is D

Solution and Explanation

Once you are told the professor conducts a quiz on Tuesday, two things become fixed for the rest of the week: the quiz mornings must be Tuesday, Wednesday and Friday, since Monday cannot also be a quiz day once Tuesday is, by the given rule, so Wednesday and Friday have to fill out the remaining two quiz mornings, and only Monday or Saturday can be the single morning that gets evaluation. Reading the answer choices against just these two facts eliminates four of them almost instantly.

  1. Monday morning, Monday afternoon, Friday morning, Friday afternoon: This puts an evaluation on Friday morning, but Friday morning is locked in as a quiz once Tuesday is a quiz day. It also tries to use two separate mornings, Monday and Friday, for evaluation, when only one morning in the whole week is ever an evaluation morning.
  2. Monday morning, Friday afternoon, Saturday morning, Saturday afternoon: This again names two evaluation mornings, Monday and Saturday, which cannot both be true since evaluation only ever occupies a single morning across the entire week.
  3. Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon: This needs Wednesday morning to be an evaluation slot, but Wednesday morning is fixed as a quiz whenever Tuesday is a quiz day, so this cannot be correct.
  4. Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon: This makes the same mistake as the previous option, treating Wednesday morning as an evaluation slot when it must be a quiz slot.

That leaves Wednesday afternoon, Friday afternoon, Saturday morning and Saturday afternoon. Saturday morning is one of the two days, Monday or Saturday, that is free to be the evaluation morning, and choosing Saturday for evaluation means Monday becomes the consultancy morning instead. With the lecture afternoons then falling on Monday and Tuesday, the three leftover afternoons, Wednesday, Friday and Saturday, are all evaluation afternoons, exactly matching this option. Every one of the six original restrictions is satisfied by this reading of the week.

Let's summarize:

  • A quiz on Tuesday forces the quiz mornings to be Tuesday, Wednesday and Friday, since Monday is then ruled out and only Wednesday and Friday remain to complete the three quiz mornings.
  • Only one morning in the whole week is ever an evaluation morning, so any option naming two separate evaluation mornings is automatically wrong.
  • Wednesday morning can never be an evaluation slot once Tuesday is a quiz day, since Wednesday itself must be a quiz morning.

So the professor's evaluation schedule could be Wednesday afternoon, Friday afternoon, Saturday morning and Saturday afternoon, which is option (EE).

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