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In a survey of 200 college students about their language preferences: - 130 students like Hindi - 90 students like English - 70 students like Tamil - 40 students like both Hindi and English - 25 students like both Hindi and Tamil - 20 students like both English and Tamil - 15 students like all three languages - The rest dislike all three languages. How many students like only Hindi (and neither English nor Tamil)?
A65
B80
C80 (= 130 - 40 - 25 + 15 = 130 - 50 = 80)
D50
Answer & Solution
Correct answer: C. 80 (= 130 - 40 - 25 + 15 = 130 - 50 = 80)
Hindi only = n(H) - n(H∩E) - n(H∩T) + n(H∩E∩T) = 130 - 40 - 25 + 15 = 80. The +15 corrects for double subtraction of the triple-intersection.
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