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.
If the Professor conducts a quiz on Tuesday, then her schedule for evaluating quizzes could be:
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:
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
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question.
We are told the professor conducts a quiz on Tuesday morning, and we need to find which one of the given evaluation schedules, one morning slot plus three afternoon slots, she could actually be following.
Step 2: Key Formula or Approach.
Since Tuesday is a quiz day, this fixes which three days are the quiz mornings. Restriction 2 says if Monday is a quiz day, Tuesday cannot be, so since Tuesday is a quiz day here, Monday cannot also be a quiz day. That leaves Tuesday, Wednesday and Friday as the three quiz mornings, since Wednesday and Friday must fill out the remaining two quiz mornings and Saturday is never a quiz day. This also means Monday and Saturday are the two mornings left over for evaluation and consultancy, one each.
Step 3: Detailed Explanation.
Now check each option against two hard facts: there can only be one evaluation morning in total, and Wednesday morning is fixed as a quiz, never evaluation.
Option (AA), Monday morning, Monday afternoon, Friday morning, Friday afternoon: this lists a morning evaluation on Friday, but Friday morning must be a quiz here, not evaluation, so it is out. It also gives two separate morning evaluations, Monday and Friday, which breaks the rule of exactly one evaluation morning.
Option (BB), Monday morning, Friday afternoon, Saturday morning, Saturday afternoon: this again lists two morning evaluations, Monday and Saturday, but only one morning can ever be an evaluation morning, so it is out.
Option (CC), Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon: this needs Wednesday morning to be an evaluation, but we just fixed Wednesday morning as a quiz whenever Tuesday is a quiz day, so it is out.
Option (DD), Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon: this also needs Wednesday morning to be an evaluation, which again contradicts Wednesday always being a quiz morning here, so it is out.
Option (EE), Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon: here the single evaluation morning is Saturday, which is allowed since Saturday is one of the two leftover mornings, with Monday then becoming the consultancy morning. The lecture afternoons in this case are Monday and Tuesday, leaving Wednesday, Friday and Saturday afternoons for evaluation, which is exactly what this option lists. Every restriction checks out, so this is a genuinely valid schedule.
Step 4: Final Answer.
Only option (EE), evaluating on Wednesday afternoon, Friday afternoon, Saturday morning and Saturday afternoon, is consistent with a quiz on Tuesday and all six restrictions. \[ \boxed{\text{Option (EE)}} \]
We are told the professor conducts a quiz on Tuesday morning, and we need to find which one of the given evaluation schedules, one morning slot plus three afternoon slots, she could actually be following.
Step 2: Key Formula or Approach.
Since Tuesday is a quiz day, this fixes which three days are the quiz mornings. Restriction 2 says if Monday is a quiz day, Tuesday cannot be, so since Tuesday is a quiz day here, Monday cannot also be a quiz day. That leaves Tuesday, Wednesday and Friday as the three quiz mornings, since Wednesday and Friday must fill out the remaining two quiz mornings and Saturday is never a quiz day. This also means Monday and Saturday are the two mornings left over for evaluation and consultancy, one each.
Step 3: Detailed Explanation.
Now check each option against two hard facts: there can only be one evaluation morning in total, and Wednesday morning is fixed as a quiz, never evaluation.
Option (AA), Monday morning, Monday afternoon, Friday morning, Friday afternoon: this lists a morning evaluation on Friday, but Friday morning must be a quiz here, not evaluation, so it is out. It also gives two separate morning evaluations, Monday and Friday, which breaks the rule of exactly one evaluation morning.
Option (BB), Monday morning, Friday afternoon, Saturday morning, Saturday afternoon: this again lists two morning evaluations, Monday and Saturday, but only one morning can ever be an evaluation morning, so it is out.
Option (CC), Monday afternoon, Wednesday morning, Wednesday afternoon, Saturday afternoon: this needs Wednesday morning to be an evaluation, but we just fixed Wednesday morning as a quiz whenever Tuesday is a quiz day, so it is out.
Option (DD), Wednesday morning, Wednesday afternoon, Friday afternoon, Saturday afternoon: this also needs Wednesday morning to be an evaluation, which again contradicts Wednesday always being a quiz morning here, so it is out.
Option (EE), Wednesday afternoon, Friday afternoon, Saturday morning, Saturday afternoon: here the single evaluation morning is Saturday, which is allowed since Saturday is one of the two leftover mornings, with Monday then becoming the consultancy morning. The lecture afternoons in this case are Monday and Tuesday, leaving Wednesday, Friday and Saturday afternoons for evaluation, which is exactly what this option lists. Every restriction checks out, so this is a genuinely valid schedule.
Step 4: Final Answer.
Only option (EE), evaluating on Wednesday afternoon, Friday afternoon, Saturday morning and Saturday afternoon, is consistent with a quiz on Tuesday and all six restrictions. \[ \boxed{\text{Option (EE)}} \]
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