In a class of students, 6 students can speak Hindi, 15 can speak English, and…
2019
In a class of students, 6 students can speak Hindi, 15 can speak English, and 6 can speak French. No student can speak any other language. If there are 2 students who can speak only two languages and one student who can speak all three languages, find the total number of students in the class.
Answer: A. 23 — Given: Hindi = 6, English = 15, French = 6. Exactly two languages = 2. All three languages = 1. Method (using total language-counts): Sum of individual…
- A.
23
- B.
26
- C.
22
- D.
24
Attempted by 133 students.
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Correct answer: A
Given: Hindi = 6, English = 15, French = 6. Exactly two languages = 2. All three languages = 1.
Method (using total language-counts):
Sum of individual language counts = 6 + 15 + 6 = 27.
This sum equals (number who speak exactly one language) + 2*(number who speak exactly two languages) + 3*(number who speak all three languages).
Let s1 be the number who speak exactly one language. Then s1 + 2*2 + 3*1 = 27 → s1 + 4 + 3 = 27 → s1 = 20.
Total students = s1 + (students who speak exactly two) + (students who speak all three) = 20 + 2 + 1 = 23.
Alternative (union formula) check:
Sum of pairwise intersections (including the triple-counted student in each pair) = (students who speak exactly two) + 3*(students who speak all three) = 2 + 3*1 = 5.
By the union formula: total = 6 + 15 + 6 − 5 + 1 = 23, matching the previous result.
Answer: 23 students