Test Index

IPMAT 2026 Exam Solved Papers

Question Numbers: 2, 4, 12

Five friends A, B, C, D, and E go on a trip together. Each of them likes at least one of the following three activities: Countryside Sightseeing, Shopping, and Adventure Sports such that:

- No two friends like exactly the same set of activities.

- A, B and E like exactly two activities each.

- D likes only Countryside Sightseeing.

- C likes more number of activities compared to D.

Question : 2 of 90

Marks: +1, -0

The number of friends that like Countryside Sightseeing is

\_\_\_\_

Your Answer:

Validate

Solution:

Each of the 5 friends likes at least one of {Countryside, Shopping, Adventure}. Possible activity-sets (non-empty subsets of a 3-element set) = 7.

- D likes only Countryside.

- A, B, E each like exactly two activities (3 possible 2-element sets:

\{\mathrm{C}, \mathrm{S}\},\{\mathrm{C}, \mathrm{A}\},\{\mathrm{S}, \mathrm{A}\}

). Since all three must be distinct, they cover all three 2-element subsets.

- C likes more activities than D (more than 1). C cannot duplicate the 2-element sets already taken, so C likes all three.

Friends liking Countryside: D, the two of A/B/E whose 2-set contains C, and C. That gives 4.

Go to Question:

Prev Question

Next Question