# Quantitative Aptitude – Set Theory – 190 students have to choose at least one elective

## XAT 2020 Exam Paper – Quantitative Aptitude – Set Theory – 190 students have to choose at least one elective

Instructions
190 students have to choose at least one elective and at most two electives from a list of three electives: E1, E2 and E3. It is found that the number of students choosing E1 is half the number of students choosing E2, and one third the number of students choosing E3. Moreover, the number of students choosing two electives is 50.

Q. Which of the following CANNOT be obtained from the given information?
1. Number of students choosing E1
2. Number of students choosing either E1 or E2 or both, but not E3
3. Number of students choosing both E1 and E2
4. Number of students choosing E3
5. Number of students choosing exactly one elective

Answer: Number of students choosing both E1 and E2

Q. In addition to the given information, which of the following information is NECESSARY and SUFFICIENT to compute the number of students choosing only E1, only E2 and only E3?
1. Number of students choosing only E2, and number of students choosing both E2 and E3
2. Number of students choosing both E1 and E2, number of students choosing both E2 and E3, and number of students choosing both E3 and E1
3. Number of students choosing only E1, and number of students choosing both E2 and E3
4. No extra information is necessary
5. Number of students choosing both E1 and E2

Answer: Number of students choosing only E2, and number of students choosing both E2 and E3

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