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CAT 2025 Lesson : Class Discussion: Modern Maths - Set Theory: 9 to 16
Class Discussion: Set theory
Question 9
In a class of 120 students, one-fourth of the class passed in both maths and science. The number of students who passed in science exceeded the number of students who passed in maths by the same number as that of the students who failed in both subjects. How many students passed in science?
| 60 | ||
| 75 | ||
| 84 | ||
| 90 |
Question 10
In a class of 120 students, one-fourth of the class passed in both maths and science. The number of students who passed in science exceeded the number of students who passed in maths by the same number as that of the students who failed in both subjects. How many students passed in maths?
| 45 | ||
| 57 | ||
| 60 | ||
| Cannot be determined |
Question 11
Alpha, Beta and Gamma are the three brands produced by a soap manufacturer. A survey was conducted among 180 residents of a neighbourhood on the use of these soaps. The number of residents who have used Alpha, Beta and Gamma brands were 70, 80 and 120 respectively. 40 residents have used Alpha and Beta brands, 60 residents have used Beta and Gamma brands and 55 residents have used Alpha and Gamma brands. What is the maximum possible number of residents who have not used any of these soaps?
| 25 | ||
| 30 | ||
| 35 | ||
| 40 |
Question 12
Alpha, Beta and Gamma are the three brands produced by a soap manufacturer. A survey was conducted among 180 residents of a neighbourhood on the use of these soaps. The number of residents who have used Alpha, Beta and Gamma brands were 70, 80 and 120 respectively. 40 residents have used Alpha and Beta brands, 60 residents have used Beta and Gamma brands and 55 residents have used Alpha and Gamma brands. What is the least possible number of residents who have used Alpha or Beta brands but not the Gamma brand?
| 20 | ||
| 30 | ||
| 40 | ||
| 50 |
Question 13
Alpha, Beta and Gamma are the three brands produced by a soap manufacturer. A survey was conducted among 180 residents of a neighbourhood on the use of these soaps. The number of residents who have used Alpha, Beta and Gamma brands were 70, 80 and 120 respectively. 40 residents have used Alpha and Beta brands, 60 residents have used Beta and Gamma brands and 55 residents have used Alpha and Gamma brands. What is the maximum possible number of residents who have used exactly one of the brands?
| 35 | ||
| 70 | ||
| 80 | ||
| 100 |
Question 14
A school for percussionists has 79 enrolled students, all of whom can play at least one among the Tabla, the Mridangam and the Dhol. 16, 15 and 19 students can play only the Tabla, only the Mridangam and only the Dhol respectively. The number of students who can play the Tabla is 5 more than the number of students who can play the Mridangam, which in turn is 5 more than the number of students who can play the Dhol. Three students can play all the three instruments. How many students do not play the Tabla?
Answer: 37
Answer: 37
Question 15
A school for percussionists has 79 enrolled students, all of whom can play at least one among the Tabla, the Mridangam and the Dhol. 16, 15 and 19 students can play only the Tabla, only the Mridangam and only the Dhol respectively. The number of students who can play the Tabla is 5 more than the number of students who can play the Mridangam, which in turn is 5 more than the number of students who can play the Dhol. Three students can play all the three instruments. How many students play the Mridangam and the Dhol?
Answer: 6
Answer: 6
Question 16
A school for percussionists has 79 enrolled students, all of whom can play at least one among the Tabla, the Mridangam and the Dhol. 16, 15 and 19 students can play only the Tabla, only the Mridangam and only the Dhol respectively. The number of students who can play the Tabla is 5 more than the number of students who can play the Mridangam, which in turn is 5 more than the number of students who can play the Dhol. Three students can play all the three instruments. How many students play the Mridangam but not the Tabla?
Answer: 18
Answer: 18
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