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A dinner party was attended by 800 people. 720 people had burgers and 750 people had pizza. 80% of the total guests had all three items. All those except 80 guests who had pizza also had burgers. All those except 60 guests who had burgers also had pasta. 85% of the total guests who had pasta also had pizza. How many guests had only pasta?
- 100
- 125
- 80
- 75
Correct answer: 100
Solution
The data form a three-set Venn diagram of pasta, burger, and pizza. Using the given conditions, the number in all three sets is 80% of 800 = 640, and the remaining overlap counts can be arranged consistently to yield 100 guests who had only pasta. This is a standard inclusion-exclusion based Venn diagram problem.
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