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.
Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
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 \(\frac{160}{250}\times100=64\)
What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
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 \(\frac{210}{250}\times100=84\)
What percentage of the students surveyed who supported both proposals A and B preferred Sunita as student union president?
- 50
- 40
- 20
- 25
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 \(\frac{50}{250}\times100=50\)
How many of the students surveyed supported proposal B, did not support proposal A and preferred Ragini as student union president?
- 200
- 150
- 210
- 40
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.
Top Questions on Conclusion
- A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam (A), Bashir (B), Chhavi (C), and Davies (D), sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs they are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction they choose to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known: 1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6. 2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2. At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. & nbsp;
The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher.
1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4.
2. Dolly and Falguni were the only employees who got the same rating across all the quarters.
3. The following is known about ratings given by Lalu (Novice manager):
– Bunty received a rating of 1 in Quarter 2. & nbsp;
– Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.- Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively. Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q. Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi - There are only four neighbourhoods in a city-Levmisto, Tyhrmisto,Pesmisto and Kitmisto. During the onset of a pandemic,the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0,1,2 or 3.
The following facts are also known:
1. There was at least one new case in every neighbourhood on Day 1.
2. On each of the five days, there were more new cases in Kitmisto than in Pesmisto.
3. The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.
4. The maximum number of new cases in a day in Pesmisto was 2 and this happenedonly once during the five-day period.
5. Kitmisto is the only place to have 3 new cases on Day 2.
6. The total numbers of new cases in Levmisto,Tyhrmisto,Pesmisto and Kitmisto over the five-day period were 12,12,5 and 14 respectively. - The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department.
Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.
The following additional facts are also known.
1. Seminars by students from Economics are scheduled in each of the four slots.
2. A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
3. F is an Anthropology student whose seminar is scheduled at 10:30 am.
4. The seminar of a Sociology student is scheduled at 9:00 am.
5. B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.
6. P, who is guiding both B and C, has students scheduled in the first two slots.
7. A and G are scheduled in two consecutive slots.
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- In the sequence 1, 3, 5, 7, ..., k, ..., 57, the sum of the numbers up to k, excluding k, is equal to the sum of the numbers from k up to 57, also excluding k. What is k?
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\[ \begin{cases} x \geq y \geq 3 \\ x + y \leq 14 \end{cases} \]
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- The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was
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