Of the 45 households in a certain neighborhood, 28 subscribe to Newspaper Q, 17 subscribe to Newspaper R, 12 subscribe...
GMAT Advanced Topics : (AT) Questions
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Of the 45 households in a certain neighborhood, 28 subscribe to Newspaper Q, 17 subscribe to Newspaper R, 12 subscribe to Newspaper S, 7 subscribe to both Q and R, 8 subscribe to both Q and S, and 9 subscribe to both R and S. The number of households who subscribe to all three newspapers is equal to the number of households who subscribe to none of the three newspapers. If 39 of the households subscribe to at least one of the three newspapers, how many households subscribe to only one of the newspapers?
Solution
- Translate the problem requirements: We need to find households subscribing to exactly one newspaper.
- Use the key constraint: Number subscribing to all three equals number subscribing to none, so both are 6.
- Apply inclusion–exclusion: Total = 28 + 17 + 12 − 7 − 8 − 9 + 6 = 39, matches given.
- Calculate only-one subscriptions: Q only = 28 − 7 − 8 + 6 = 19; R only = 17 − 7 − 9 + 6 = 7; S only = 12 − 8 − 9 + 6 = 1; total = 27.
Answer Choices Explained
A
15
B
21
C
27
D
33
E
46
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