In a class of 100 students, every student has passed in one or more of the three subjects, i.e. History, Economics and English. Among all the students, 24 students have passed in English only, 14 students have passed in History only, 11 students have passed in both English and Economics only, and 12 students have passed in both English and History only. A total of 50 students have passed in History. If only 5 students have passed in all three subjects, then how many students have passed in Economics only?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 15
| Understanding |
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Number of students who have passed in English only = n(E) only = 24 Number of students who have passed in History only = n(H) only = 14 Number of students who have passed both in English and Economics = n(E ∩ Eco) = 11 Number of students who have passed both in English and History = n(E ∩ H) = 12 Total number of students who have passed in History = n(H) = 50 Number of students who have passed in all three subjects = n(E ∩ Eco ∩ H) = 5 Number of students who passed in only History and Economics = n(Eco ∩ H) = 50 - (12 + 14 + 5) = 50 - 31 = 19 Thus, total number of students who passed in Econmics only = n(E) = 100 - (11 + 24 + 5 + 12 + 19 + 14) = 100 - 85 = 15 Hence, option 4 is the correct answer. |
