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.
Which one of the following must be a day on which the professor lectures?
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?
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
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question.
We need to find the one day, among Monday, Tuesday, Wednesday, Friday and Saturday, that the professor must lecture on, no matter which valid version of her weekly schedule she is actually following.
Step 2: Key Formula or Approach.
The two lecture afternoons must fall on two calendar days in a row. Among the five working days, Wednesday to Friday is not a true consecutive pair since Thursday sits between them and is not a working day, and Friday to Saturday is ruled out since Saturday never has a lecture. So the only two possible lecture pairs left are Monday-Tuesday and Tuesday-Wednesday.
Step 3: Detailed Explanation.
Compare these two possible pairs directly: Monday-Tuesday and Tuesday-Wednesday. Monday appears in only the first pair, and Wednesday appears in only the second pair, so neither of them is guaranteed. Friday and Saturday do not appear in either pair at all, and restriction 6 explicitly rules out Saturday lectures anyway, so they can never be must-lecture days. Tuesday, however, appears in both possible pairs. Whether the professor's actual lecture pair turns out to be Monday-Tuesday or Tuesday-Wednesday, Tuesday is always one of the two days she lectures on.
Step 4: Final Answer.
Since every valid schedule has its lecture pair include Tuesday, the day she must lecture on is Tuesday. \[ \boxed{\text{Tuesday}} \]
We need to find the one day, among Monday, Tuesday, Wednesday, Friday and Saturday, that the professor must lecture on, no matter which valid version of her weekly schedule she is actually following.
Step 2: Key Formula or Approach.
The two lecture afternoons must fall on two calendar days in a row. Among the five working days, Wednesday to Friday is not a true consecutive pair since Thursday sits between them and is not a working day, and Friday to Saturday is ruled out since Saturday never has a lecture. So the only two possible lecture pairs left are Monday-Tuesday and Tuesday-Wednesday.
Step 3: Detailed Explanation.
Compare these two possible pairs directly: Monday-Tuesday and Tuesday-Wednesday. Monday appears in only the first pair, and Wednesday appears in only the second pair, so neither of them is guaranteed. Friday and Saturday do not appear in either pair at all, and restriction 6 explicitly rules out Saturday lectures anyway, so they can never be must-lecture days. Tuesday, however, appears in both possible pairs. Whether the professor's actual lecture pair turns out to be Monday-Tuesday or Tuesday-Wednesday, Tuesday is always one of the two days she lectures on.
Step 4: Final Answer.
Since every valid schedule has its lecture pair include Tuesday, the day she must lecture on is Tuesday. \[ \boxed{\text{Tuesday}} \]
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