Question

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.

On Wednesdays, the professor could be scheduled to:

• A. Work on a consultancy project in the morning and conduct a quiz in the afternoon
• B. Lecture in the morning and evaluate quizzes in the afternoon
• C. Conduct a quiz in the morning and lecture in the afternoon
• D. Conduct a quiz in the morning and work on a consultancy project in the afternoon

Hint:

Work out first which activities are even allowed to sit in a morning slot and which are allowed in an afternoon slot, before checking each option.

Answer 1

The Correct Option is C

This question is testing whether you can spot which one of five possible Wednesday routines actually fits the rules, without redrawing the whole week. A faster route is to first work out what kind of activity is even allowed in a morning slot and in an afternoon slot, then test each option against that filter.

1. Work on a consultancy project in the morning and conduct a quiz in the afternoon: Quizzes are only ever scheduled in a morning slot in this problem, since three mornings are quiz mornings and the afternoon slots are fully used up by lectures and evaluation. A quiz in the afternoon breaks that, so this option is out.
2. Lecture in the morning and evaluate quizzes in the afternoon: The five mornings must supply exactly 3 quiz mornings, 1 evaluation morning and 1 consultancy morning, and 3 + 1 + 1 already equals all five mornings. There is no room left for a lecture in any morning, so this option is out.
3. Conduct a quiz in the morning and lecture in the afternoon: Wednesday is always one of the three quiz mornings, because the quiz mornings must be Monday, Wednesday, Friday if Monday is a quiz day, or Tuesday, Wednesday, Friday if it is not, and both sets contain Wednesday. Wednesday can also be one of the two consecutive lecture afternoons, in the case where the lecture pair is Tuesday and Wednesday rather than Monday and Tuesday. Both halves check out together, so this option is a genuine possibility.
4. Conduct a quiz in the morning and work on a consultancy project in the afternoon: The five afternoons must supply exactly 2 lecture afternoons and 3 evaluation afternoons, which already adds up to all five. A consultancy project in the afternoon has no slot to sit in, so this option is out.

The only option that survives the filter is quiz in the morning with lecture in the afternoon, which matches the schedule where the professor's two lecture afternoons fall on Tuesday and Wednesday.

Let's summarize:

• Mornings only ever hold a quiz, an evaluation, or a consultancy project; lectures never sit in a morning.
• Afternoons only ever hold a lecture or an evaluation; quizzes and consultancy work never sit in an afternoon.
• Wednesday morning is a quiz in every valid version of the week, and Wednesday afternoon is a lecture whenever the two lecture days chosen are Tuesday and Wednesday.

So the professor could be scheduled to conduct a quiz in the morning and lecture in the afternoon on Wednesday, which is option (CC).