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In a city with 10,000 households, it is observed that 40% of the households subscribe to newspaper A, 20% subscribe to newspaper B, and 10% subscribe to newspaper C. Also, 5% subscribe to both A and B, 3% subscribe to both B and C, and 4% subscribe to both A and C. If 2% of the households subscribe to all three newspapers, then

1. 3,300 households subscribe to A only
2. 1,400 households subscribe to B only
3. 4,000 households subscribe to none of A, B and C
4. All of the above statements are true

Correct answer: All of the above statements are true

Solution

With N=10000: A-only = A-AB-AC+ABC = 4000-500-400+200 = 3300; B-only = 2000-500-300+200 = 1400; union = 4000+2000+1000-500-300-400+200 = 6000, so none = 10000-6000 = 4000. All three statements hold, so the correct choice is 'All of the above are true'.

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