Let’s solve each question step by step using the Venn diagram numbers.
We have three clubs: Math, Arts, and Music. The overlapping regions show students who joined more than one club.
Here are the numbers from the diagram:
- Only Math: 22
- Only Arts: 15
- Only Music: 18
- Math & Arts only (not Music): 8
- Math & Music only (not Arts): 6
- Arts & Music only (not Math): 5
- All three clubs: 12
- Outside all clubs (joined none): 7
Now let’s answer each question:
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1. How many students joined only the math club?
Look at the part of the Math circle that doesn’t overlap with any other circle → that’s
22.
✔ Answer: 22
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2. How many students joined the arts club?
This means ALL students in the Arts circle — including those who also joined other clubs.
Add up:
- Only Arts: 15
- Arts & Math only: 8
- Arts & Music only: 5
- All three: 12
Total = 15 + 8 + 5 + 12 =
40
✔ Answer: 40
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3. How many students joined a club but did not join the math or arts clubs?
That means they joined ONLY the music club (since if they joined math or arts, we exclude them).
“Only Music” is
18.
(Note: If someone joined Music AND Math, or Music AND Arts, or all three — they’re excluded because they joined math or arts.)
So yes — only the “only Music” section counts →
18
✔ Answer: 18
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4. How many students joined both the arts club and the music club?
This includes:
- Arts & Music only (not Math): 5
- All three clubs: 12
Total = 5 + 12 =
17
✔ Answer: 17
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5. How many students did not join any clubs?
That’s the number outside all circles →
7
✔ Answer: 7
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6. How many students joined all the three clubs?
That’s the center where all three circles overlap →
12
✔ Answer: 12
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Final Answer:
1. 22
2. 40
3. 18
4. 17
5. 7
6. 12
Parent Tip: Review the logic above to help your child master the concept of venn diagram practice worksheet.
