Question:
A junior school is offering five after-school activities - Karate, Handwork, Music Dance, and Gymnastics. Each of the five students – Leena, Megan, Neha, Omar, and Pixia – has subscribed to at least one activity. As per the school rules, anyone who subscribes to Gymnastics must also subscribe to Dance. Karate and Handwork must always be subscribed together. Music and Dance cannot be subscribed together. The following information is available about the student's subscriptions:
- Megan subscribed to four activities.
- Leena subscribed to Gymnastics but not Karate.
- Pixie subscribed to only one activity and is the only one who subscribes to that activity.
- Omar subscribed to three activities.
- Neha subscribed to only one activity.
How many activities are subscribed by exactly two people each?
A junior school is offering five after-school activities - Karate, Handwork, Music Dance, and Gymnastics. Each of the five students – Leena, Megan, Neha, Omar, and Pixia – has subscribed to at least one activity. As per the school rules, anyone who subscribes to Gymnastics must also subscribe to Dance. Karate and Handwork must always be subscribed together. Music and Dance cannot be subscribed together. The following information is available about the student's subscriptions:
- Megan subscribed to four activities.
- Leena subscribed to Gymnastics but not Karate.
- Pixie subscribed to only one activity and is the only one who subscribes to that activity.
- Omar subscribed to three activities.
- Neha subscribed to only one activity.
How many activities are subscribed by exactly two people each?
- Megan subscribed to four activities.
- Leena subscribed to Gymnastics but not Karate.
- Pixie subscribed to only one activity and is the only one who subscribes to that activity.
- Omar subscribed to three activities.
- Neha subscribed to only one activity.
How many activities are subscribed by exactly two people each?
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In problems involving subscriptions or memberships, break down the conditions step by step and keep track of overlapping memberships.
Updated On: Oct 7, 2025
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The Correct Option is D
Solution and Explanation
Given the constraints and conditions, we can infer the following:
- Megan subscribed to four activities, which likely includes Dance and Gymnastics (because Gymnastics requires Dance).
- Leena subscribed to Gymnastics but not Karate, so she must have subscribed to Dance as well (since Gymnastics and Dance must go together).
- Pixie subscribed to only one activity, and it is unique to her, which means she must have subscribed to Handwork.
- Omar subscribed to three activities, and since Megan and Leena's subscriptions cover most activities, Omar must have subscribed to Karate, Handwork, and one other.
- Neha subscribed to only one activity, so she could have subscribed to either Karate or Handwork, but since Handwork is also tied to Karate, she likely subscribed to Karate.
By deducing the subscriptions, we find that Karate and Handwork are subscribed by exactly two people (Omar and Leena), Dance and Gymnastics are subscribed by two people, and Music and Handwork are each subscribed by exactly two people.
Thus, the total number of activities subscribed by exactly two people is \( \boxed{3} \).
- Megan subscribed to four activities, which likely includes Dance and Gymnastics (because Gymnastics requires Dance).
- Leena subscribed to Gymnastics but not Karate, so she must have subscribed to Dance as well (since Gymnastics and Dance must go together).
- Pixie subscribed to only one activity, and it is unique to her, which means she must have subscribed to Handwork.
- Omar subscribed to three activities, and since Megan and Leena's subscriptions cover most activities, Omar must have subscribed to Karate, Handwork, and one other.
- Neha subscribed to only one activity, so she could have subscribed to either Karate or Handwork, but since Handwork is also tied to Karate, she likely subscribed to Karate.
By deducing the subscriptions, we find that Karate and Handwork are subscribed by exactly two people (Omar and Leena), Dance and Gymnastics are subscribed by two people, and Music and Handwork are each subscribed by exactly two people.
Thus, the total number of activities subscribed by exactly two people is \( \boxed{3} \).
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