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

Step 1: Understanding the Question.
We are told how Professor Mukhopadhay fills her mornings and afternoons across five working days: Monday, Tuesday, Wednesday, Friday and Saturday. We need to work out what her Wednesday could actually look like, given six restrictions on quizzes, evaluation, lectures and consultancy work.

Step 2: Key Formula or Approach.
Count the activities. Across the five mornings, quizzes take up 3 mornings, evaluation takes up 1 morning, and consultancy takes up 1 morning. That is 3 + 1 + 1 = 5, which is every morning there is. So lecturing never happens in a morning, and Wednesday morning must be quiz, evaluation or consultancy. Across the five afternoons, lectures take up 2 (on two consecutive calendar days) and evaluation takes up 3. That is 2 + 3 = 5, every afternoon there is. So quiz and consultancy never happen in an afternoon, and Wednesday afternoon must be lecture or evaluation.

Step 3: Detailed Explanation.
Now pin down the quiz mornings. They must be 3 of Monday, Tuesday, Wednesday and Friday, since Saturday never has a quiz. If she quizzes on Monday, she cannot quiz on Tuesday, so the 3 quiz mornings have to be Monday, Wednesday and Friday. If she does not quiz on Monday, all three of Tuesday, Wednesday and Friday must be quiz mornings, since there is no other way to get 3. Either way, Wednesday morning is always a quiz.
Next, look at the lecture afternoons. They must fall on two calendar days in a row, both from the working days. Wednesday to Friday is not consecutive because Thursday sits in between and is not a working day, and Friday to Saturday is ruled out because Saturday never lectures. So the only possible lecture pairs are Monday-Tuesday or Tuesday-Wednesday. In the Monday-Tuesday case, Wednesday afternoon is not a lecture, so it must be evaluation. In the Tuesday-Wednesday case, Wednesday afternoon is a lecture. Both of these are genuine, fully consistent schedules, so Wednesday afternoon can honestly be either evaluation or lecture, but Wednesday morning is always a quiz.
Checking each option against this: option (AA) needs a quiz in the afternoon, which we showed is impossible. Option (BB) needs a lecture in the morning, also impossible. Option (DD) needs consultancy in the afternoon, impossible. Option (EE) needs evaluation in the morning, but Wednesday morning is always a quiz, so this fails too. Only option (CC), quiz in the morning and lecture in the afternoon, matches one of the two valid full schedules we found.

Step 4: Final Answer.
Wednesday morning is always a quiz, and Wednesday afternoon can be a lecture in the Tuesday-Wednesday lecture case, so the professor could be scheduled to conduct a quiz in the morning and lecture in the afternoon. \[ \boxed{\text{Option (CC)}} \]