Question:medium

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.

Which one of the following must be a day on which the professor lectures?

Show Hint

List the only two possible pairs of consecutive lecture days first, then see which single day appears in both.
Updated On: Jul 10, 2026
  • Monday
  • Tuesday
  • Wednesday
  • Friday
Show Solution

The Correct Option is B

Solution and Explanation

This question is really asking which single day cannot be avoided as a lecture day, across every possible valid schedule the professor could run. The fastest way to answer it is to pin down every day that could theoretically host a lecture afternoon, and see which one shows up in all of them.

  1. Monday: Monday can be a lecture afternoon, but only when the two consecutive lecture days chosen are Monday and Tuesday. If the professor instead picks Tuesday and Wednesday as her lecture pair, Monday never lectures at all, so Monday is not guaranteed.
  2. Tuesday: The two lecture afternoons must be two calendar days in a row, and among the working days, Wednesday to Friday fails because Thursday breaks the run, while Friday to Saturday fails because Saturday never lectures. That leaves exactly two workable pairs, Monday-Tuesday and Tuesday-Wednesday, and Tuesday belongs to both of them. So no matter which pair the professor actually follows, Tuesday is always a lecture day.
  3. Wednesday: Wednesday only lectures when the chosen pair is Tuesday-Wednesday. If the pair is Monday-Tuesday instead, Wednesday never gets a lecture, so it is not guaranteed either.
  4. Friday: Friday cannot be part of any valid consecutive lecture pair, since Wednesday-Friday is broken by the non-working Thursday and Friday-Saturday is blocked by Saturday never lecturing. Friday therefore never lectures in any valid schedule.

Saturday can be eliminated immediately too, since the puzzle states directly that she never lectures on Saturday. Only Tuesday belongs to both of the two workable lecture pairs, Monday-Tuesday and Tuesday-Wednesday, so it is the one day that is a lecture day in every possible version of the week.

Let's summarize:

  • Only two pairs of consecutive working days can ever host the lecture afternoons: Monday-Tuesday and Tuesday-Wednesday.
  • Monday and Wednesday each appear in only one of those two pairs, so neither is guaranteed.
  • Friday and Saturday never appear in a workable lecture pair at all.

Tuesday is the only day common to both possible lecture pairs, so it is the day the professor must lecture on, which is option (BB).

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