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A survey shows that 73% of people in an office like coffee and 65% like tea. If x denotes the percentage who like both coffee and tea, which of the following values of x is NOT possible?

1. 63
2. 38
3. 54
4. 86

Correct answer: 86

Solution

From the inclusion-exclusion principle: P(C union T) = 73 + 65 - x <= 100, so x >= 38. Also x cannot exceed either set: x <= min(73,65) = 65. Therefore 38 <= x <= 65. Checking options: 63 in [38,65] — valid; 38 in [38,65] — valid (boundary); 54 in [38,65] — valid; 86 > 65 — NOT valid.

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