Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 This diagram shows 30 students. How many play the guitar?
Show worked solution
7 play guitar only and 7 play both, so 14 play the guitar.
2 Using the diagram, write how many students play both instruments, and how many play neither.
Show worked solution
The overlap holds 7, and the region outside both circles holds 5.
3 25 people like apples, 18 like pears, and 10 like both. How many like at least one of the two?
Show worked solution
25 + 18 − 10 = 33.
Level 2 · Core
4 In a class of 28, 16 study French, 13 study German and 6 study both. How many study neither language?
Show worked solution
16 + 13 − 6 = 23 study at least one, so 28 − 23 = 5 study neither.
5 In a group of 40, 22 own a bike and 19 own a scooter, and 9 own both. Write how many own at least one, and how many own neither.
Show worked solution
22 + 19 − 9 = 32 own at least one, so 40 − 32 = 8 own neither.
6 Of 30 students, 18 play piano and 7 play both piano and guitar. How many play piano but not guitar?
Show worked solution
18 − 7 = 11.
Level 3 · Challenge
7 This diagram shows a sports club.1 2 members do all three sports.
2 9 members run.
3 26 members are shown altogether.
Which statements are correct?
2 9 members run.
3 26 members are shown altogether.
Which statements are correct?
Show worked solution
The centre holds 2 (1 ✓). Runs is 4 + 3 + 2 + 2 = 11, not 9 (2 ✗). All seven regions give 4 + 6 + 5 + 3 + 2 + 4 + 2 = 26 (3 ✓). 1 and 3.
8 In a group of 50 people, 30 read fiction, 24 read non-fiction, and 6 read neither. Write how many read at least one kind, and how many read both.
Show worked solution
50 − 6 = 44 read at least one. Then 30 + 24 − both = 44, so both = 54 − 44 = 10.
9 In a class of 32, every student studies at least one of art and music. 20 study art and 19 study music. How many study both?
Show worked solution
20 + 19 − both = 32, so both = 39 − 32 = 7.