UCAT three-set Venn diagrams
Fill the middle first: the number in all three. Then each pair region is the pair count minus the middle. Each single region is its total minus its two pair regions and the middle. Try two below.
Decision Making · Question 1 of 20:00 / 1:03
Of 53 members at the Alder club, 24 swim, 21 cycle and 18 run. 7 swim and cycle, 6 swim and run, and 5 cycle and run. Each of these pair counts includes the 2 members who do all three. How many swim only?
Worked answers
1. Of 53 members at the Alder club, 24 swim, 21 cycle and 18 run. 7 swim and cycle, 6 swim and run, and 5 cycle and run. Each of these pair counts includes the 2 members who do all three. How many swim only?
Answer: D: 13
- Swimming only = 24 − 7 − 6 + 2.
- Swimming only = 13.
2. Of 62 members at the Birch club, 28 swim, 26 cycle and 22 run. 9 swim and cycle, 8 swim and run, and 7 cycle and run. Each of these pair counts includes the 3 members who do all three. How many do exactly two activities?
Answer: C: 15
- Pair-only counts = 6, 5 and 4.
- Exactly two = 6 + 5 + 4 = 15.
Ready for the whole test? Sit the full free UCAT mock: 184 questions, marked by subtest.
Fill it in this order
| Region | Count |
|---|---|
| All three | Given |
| Swim and cycle only | Swim-and-cycle count − all three |
| Swim only | Swim total − both swim pairs + all three |
| None | Everyone − every region inside |
"Swim only" = swim − (swim and cycle) − (swim and run) + all three. The centre was taken away twice, so add it back once.
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