Comprehension
Students in a college are discussing two proposals --
A: a proposal by the authorities to introduce dress code on campus, and
B: a proposal by the students to allow multinational food franchises to set up outlets on college campus.
A student does not necessarily support either of the two proposals.
In an upcoming election for student union president, there are two candidates in fray: Sunita and Ragini. Every student prefers one of the two candidates.
A survey was conducted among the students by picking a sample of 500 students.
The following information was noted from this survey.
1. 250 students supported proposal A and 250 students supported proposal B.
2. Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.
3. Among those who preferred Ragini, 30% supported proposal A.
4. 20% of those who supported proposal B preferred Sunita.
5. 40% of those who did not support proposal B preferred Ragini.
6. Every student who preferred Sunita and supported proposal B also supported proposal A.
7. Among those who preferred Ragini, 20% did not support any of the proposals.
A: a proposal by the authorities to introduce dress code on campus, and
B: a proposal by the students to allow multinational food franchises to set up outlets on college campus.
A student does not necessarily support either of the two proposals.
In an upcoming election for student union president, there are two candidates in fray: Sunita and Ragini. Every student prefers one of the two candidates.
A survey was conducted among the students by picking a sample of 500 students.
The following information was noted from this survey.
1. 250 students supported proposal A and 250 students supported proposal B.
2. Among the 200 students who preferred Sunita as student union president, 80% supported proposal A.
3. Among those who preferred Ragini, 30% supported proposal A.
4. 20% of those who supported proposal B preferred Sunita.
5. 40% of those who did not support proposal B preferred Ragini.
6. Every student who preferred Sunita and supported proposal B also supported proposal A.
7. Among those who preferred Ragini, 20% did not support any of the proposals.
Question: 1
Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
Updated On: Jul 8, 2024
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Correct Answer: 64
Solution and Explanation
The groups of students who have an affinity for Sunita and Ragini are mutually exclusive sets. Consequently, the Venn diagram can be represented as follows. In total, there are 500 students.
Considering statement (2):
- Sunita = 200, leading to Ragini = 300.
Referring to statement (1):
- A(Sunita) + A(Ragini) = 250, and B(Sunita) + B(Ragini) = 250.
Derived from (2):
- A(Sunita) = 160, implying A(Ragini) = 90.
Following (4):
- B(Sunita) = 20% of 250 = 50, thereby making B(Ragini) = 200.
Based on (6):
- g(Sunita) = 50, consequently, b(Sunita) = 0, and a(Sunita) = 110. Hence, n(Sunita) = 40.
As per (7):
- n(Ragini) = 60.
Given that 250 students support B, it follows that the remaining 250 do not endorse B.
According to (5):
- (a + n) of Ragini = 40% of 250 = 100. Thus, a(Ragini) = 40.
In conclusion, the final solution is outlined as above.
The required value is \(\frac{160}{250}\times100=64\)
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Question: 2
What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
Updated On: Sep 17, 2024
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Correct Answer: 84
Solution and Explanation
The groups of students who have an affinity for Sunita and Ragini are mutually exclusive sets. Consequently, the Venn diagram can be represented as follows. In total, there are 500 students.
Considering statement (2):
- Sunita = 200, leading to Ragini = 300.
Referring to statement (1):
- A(Sunita) + A(Ragini) = 250, and B(Sunita) + B(Ragini) = 250.
Derived from (2):
- A(Sunita) = 160, implying A(Ragini) = 90.
Following (4):
- B(Sunita) = 20% of 250 = 50, thereby making B(Ragini) = 200.
Based on (6):
- g(Sunita) = 50, consequently, b(Sunita) = 0, and a(Sunita) = 110. Hence, n(Sunita) = 40.
As per (7):
- n(Ragini) = 60.
Given that 250 students support B, it follows that the remaining 250 do not endorse B.
According to (5):
- (a + n) of Ragini = 40% of 250 = 100. Thus, a(Ragini) = 40.
In conclusion, the final solution is outlined as above.
The required value is \(\frac{210}{250}\times100=84\)
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Question: 3
What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
Updated On: Aug 22, 2024
- 50
- 40
- 20
- 25
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The Correct Option is A
Solution and Explanation
The groups of students who have an affinity for Sunita and Ragini are mutually exclusive sets. Consequently, the Venn diagram can be represented as follows. In total, there are 500 students.
Considering statement (2):
- Sunita = 200, leading to Ragini = 300.
Referring to statement (1):
- A(Sunita) + A(Ragini) = 250, and B(Sunita) + B(Ragini) = 250.
Derived from (2):
- A(Sunita) = 160, implying A(Ragini) = 90.
Following (4):
- B(Sunita) = 20% of 250 = 50, thereby making B(Ragini) = 200.
Based on (6):
- g(Sunita) = 50, consequently, b(Sunita) = 0, and a(Sunita) = 110. Hence, n(Sunita) = 40.
As per (7):
- n(Ragini) = 60.
Given that 250 students support B, it follows that the remaining 250 do not endorse B.
According to (5):
- (a + n) of Ragini = 40% of 250 = 100. Thus, a(Ragini) = 40.
In conclusion, the final solution is outlined as above.
The required value is \(\frac{50}{250}\times100=50\)
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Question: 4
How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
Updated On: Aug 22, 2024
- 200
- 150
- 210
- 40
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The Correct Option is B
Solution and Explanation
The groups of students who have an affinity for Sunita and Ragini are mutually exclusive sets. Consequently, the Venn diagram can be represented as follows. In total, there are 500 students.
Considering statement (2):
- Sunita = 200, leading to Ragini = 300.
Referring to statement (1):
- A(Sunita) + A(Ragini) = 250, and B(Sunita) + B(Ragini) = 250.
Derived from (2):
- A(Sunita) = 160, implying A(Ragini) = 90.
Following (4):
- B(Sunita) = 20% of 250 = 50, thereby making B(Ragini) = 200.
Based on (6):
- g(Sunita) = 50, consequently, b(Sunita) = 0, and a(Sunita) = 110. Hence, n(Sunita) = 40.
As per (7):
- n(Ragini) = 60.
Given that 250 students support B, it follows that the remaining 250 do not endorse B.
According to (5):
- (a + n) of Ragini = 40% of 250 = 100. Thus, a(Ragini) = 40.
In conclusion, the final solution is outlined as above.
The students who supported proposal B but not A are represented by b(Sunita) and b(Ragini). Specifically, among them, those who supported Ragini are denoted by b(Ragini) = 150.
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