Eric is planning a 7-day resort vacation. He will play golf on four mornings. He also wants to play tennis but can only play tennis on days he does not play croquet. He will play croquet on any day immediately following a day that he plays golf. What is the greatest number of days he can play tennis?
A)2 B)3 C)4 D)5 E)6
C)4
To determine the greatest number of days Eric can play tennis, let's analyze the given conditions step by step:
1. Eric will play golf on four mornings: This means he has a total of 4 days occupied by golf.
2. Eric can only play tennis on days he does not play croquet: This means that if Eric plays croquet on a specific day, he cannot play tennis on that day.
3. He will play croquet on any day immediately following a day that he plays golf: This implies that if Eric plays golf on one day, he will play croquet on the very next day.
Now let's look at the possibilities:
- If Eric plays golf on Day 1, he will play croquet on Day 2. Since he played golf on Day 1, he cannot play tennis on Day 1.
- If Eric plays golf on Day 2, he will play croquet on Day 3. Since he played golf on Day 2, he cannot play tennis on Day 2.
- If Eric plays golf on Day 3, he will play croquet on Day 4. Since he played golf on Day 3, he cannot play tennis on Day 3.
- If Eric plays golf on Day 4, he will play croquet on Day 5. Since he played golf on Day 4, he cannot play tennis on Day 4.
- If Eric plays golf on Day 5, he cannot play croquet on any subsequent day because the vacation is only 7 days long. Since he played golf on Day 5, he cannot play tennis on Day 5.
Based on the given conditions, the greatest number of days Eric can play tennis is 0.
Therefore, the correct answer is A) 2, with an explanation that he cannot play tennis on any of the days due to the given conditions.