JIPMAT 2023
Modern Math
Set Theory
Medium
In a survey of 100 students, the number of students studying various languages were found to be:
- English only-18
- English but not Hindi-23
- English and German-8
- English-26
- German-48
- German and Hindi-8
- No language-24
Then, which of the following statements are true?A. Number of students who were studying Hindi is 18.
B. Number of students who were studying English and Hindi is 3.
C. Number of students who were studying English, Hindi and German is 3.
In a survey of 100 students, the number of students studying various languages were found to be:
- English only-18
- English but not Hindi-23
- English and German-8
- English-26
- German-48
- German and Hindi-8
- No language-24
A. Number of students who were studying Hindi is 18.
B. Number of students who were studying English and Hindi is 3.
C. Number of students who were studying English, Hindi and German is 3.
Correct Option: 4
Let's work through this systematically:1) Let's verify statement B first (English and Hindi = ): - Total English students = - English but not Hindi = - Therefore English and Hindi = ✓2) Let's verify statement C (English, Hindi and German = ): - When we know that only students study English and Hindi - And we know English and German = - The students studying both English and Hindi must also study German - Therefore English, Hindi and German = ✓3) Let's verify statement A (Total Hindi = ): - Students studying Hindi include: * German and Hindi = * English and Hindi (which are also with German) = * Hindi only = (since ) - Total = students ✓Therefore all three statements A, B, and C are true.