Sets, Counting & Basic Combinatorics

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All Sets Union & Intersection 2 Venn Diagrams 1 Counting Principles 1 Permutation 2 Combination
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Q1.In a group of 200 people, 90 like tennis, while 108 like cricket and 46 people like both tennis and cricket. How many people like neither tennis nor cricket?

Medium
A 44
B 48
C 62
D None of these
Union & Intersection CSS 2026

Correct Answer: B

People liking at least one sport = 90+108-46 = 152. Neither = 200-152 = 48.

Q2.The lights and brakes of 30 bicycles were tested. 27 bicycles passed the lights and 21 passed the brakes test. The lights and brakes both failed on one bicycle. How many bicycles passed both tests?

Hard
A 19
B 21
C 20
D None of these
Union & Intersection CSS 2026

Correct Answer: A

Using inclusion-exclusion: bicycles that failed at least one test = 30 - passed both. Solving with the given data gives 19 bicycles passed both tests.