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CAT 2017 Slot 2 · Quant · Permutations, Combinations and Sets · medium

In a group of 100 students, 60 drink tea, 50 drink coffee and 40 drink juice. 25 drink both tea and coffee, 20 drink both coffee and juice, 15 drink…

Single correct option

In a group of 100 students, 60 drink tea, 50 drink coffee and 40 drink juice. 25 drink both tea and coffee, 20 drink both coffee and juice, 15 drink both tea and juice, and 5 drink none of the three. How many students drink all three?
  1. A. 0
  2. B. 5
  3. C. 10
  4. D. 15
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Answer: (B) 5

Students drinking at least one = 100 − 5 = 95.

By inclusion–exclusion: n(T ∪ C ∪ J) = ΣSingle − ΣPairs + All three
95 = (60 + 50 + 40) − (25 + 20 + 15) + x = 150 − 60 + x ⇒ x = 5.

Sanity check: only-tea = 60 − 25 − 15 + 5 = 25, only-coffee = 10, only-juice = 10, all regions non-negative ✓.
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Original question written in the CAT 2017 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake