The following additional facts are known.
i. No composer who assigned item to Princess, assigned any item to Queen.
ii. No composer who assigned item to Rani, assigned any item to Samragni.
iii. The first performance was by Princess; this item was assigned by Badal.
iv. The last performance was by Rani; this item was assigned by Gagan.
v. The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
Which of the following is true?
- The second performance was composed by Dyu.
- The third performance was composed by Ashman.
- The second performance was composed by Gagan.
- The third performance was composed by Dyu.
The Correct Option is A
Solution and Explanation
Let's summarize the key deductions and conclusions made in the given information:
Total Dance Items: There are a total of 8 dance items.
First and Last Performances: The first performance was by Princess, composed by Badal, and the last performance was by Rani, composed by Gagan.
Performance Sequencing Rule: No dancer performed her second item before the performance of the first item by all the other dancers, and the dancers performed their second item in the same sequence as their first.
Compositions by Ashman: Ashman composed the fourth and fifth performances, as the first four performances were by four different composers.
Composer Assignments: If the sixth performance was composed by Badal, then the seventh would have been composed by Dyu. However, this leads to an inconsistency. Thus, the second, third, sixth, and seventh performances were composed by Dyu, Gagan, Badal, and Dyu, respectively.
Remaining Compositions: The remaining compositions (1, 8) are assigned to Ashman. The overall sequence is as follows:
- First: Princess, Badal
- Second: Samragni, Dyu
- Third: Queen, Gagan
- Fourth: Rani, Ashman
- Fifth: Rani, Ashman
- Sixth: Samragni, Badal
- Seventh: Queen, Dyu
- Eighth: Princess, Ashman
This sequence satisfies all the given conditions and constraints.
Only the statement, 'The second performance was composed by Dyu"", is true. Answer: (The second performance was composed by Dyu.)
Which of the following is FALSE?
- Queen did not perform in any item composed by Gagan.
- Rani did not perform in any item composed by Badal.
- Samragni did not perform in any item composed by Ashman.
- Princess did not perform in any item composed by Dyu.
The Correct Option is A
Solution and Explanation
Let's summarize the key deductions and conclusions made in the given information:
Total Dance Items: There are a total of 8 dance items.
First and Last Performances: The first performance was by Princess, composed by Badal, and the last performance was by Rani, composed by Gagan.
Performance Sequencing Rule: No dancer performed her second item before the performance of the first item by all the other dancers, and the dancers performed their second item in the same sequence as their first.
Compositions by Ashman: Ashman composed the fourth and fifth performances, as the first four performances were by four different composers.
Composer Assignments: If the sixth performance was composed by Badal, then the seventh would have been composed by Dyu. However, this leads to an inconsistency. Thus, the second, third, sixth, and seventh performances were composed by Dyu, Gagan, Badal, and Dyu, respectively.
Remaining Compositions: The remaining compositions (1, 8) are assigned to Ashman. The overall sequence is as follows:
- First: Princess, Badal
- Second: Samragni, Dyu
- Third: Queen, Gagan
- Fourth: Rani, Ashman
- Fifth: Rani, Ashman
- Sixth: Samragni, Badal
- Seventh: Queen, Dyu
- Eighth: Princess, Ashman
This sequence satisfies all the given conditions and constraints.
'Queen did not perform in any item composed by Gagan"" is false. Answer: (Queen did not perform in any item composed by Gagan.)
The sixth performance was composed by:
- Gagan
- Ashman
- Badal
- Dyu
The Correct Option is C
Solution and Explanation
Let's summarize the key deductions and conclusions made in the given information:
Total Dance Items: There are a total of 8 dance items.
First and Last Performances: The first performance was by Princess, composed by Badal, and the last performance was by Rani, composed by Gagan.
Performance Sequencing Rule: No dancer performed her second item before the performance of the first item by all the other dancers, and the dancers performed their second item in the same sequence as their first.
Compositions by Ashman: Ashman composed the fourth and fifth performances, as the first four performances were by four different composers.
Composer Assignments: If the sixth performance was composed by Badal, then the seventh would have been composed by Dyu. However, this leads to an inconsistency. Thus, the second, third, sixth, and seventh performances were composed by Dyu, Gagan, Badal, and Dyu, respectively.
Remaining Compositions: The remaining compositions (1, 8) are assigned to Ashman. The overall sequence is as follows:
- First: Princess, Badal
- Second: Samragni, Dyu
- Third: Queen, Gagan
- Fourth: Rani, Ashman
- Fifth: Rani, Ashman
- Sixth: Samragni, Badal
- Seventh: Queen, Dyu
- Eighth: Princess, Ashman
This sequence satisfies all the given conditions and constraints.
Sixth performance was composed by Badal. Answer: (Badal)
Which pair of performances were composed by the same composer?
- The first and the sixth
- The second and the sixth
- The first and the seventh
- The third and the seventh
The Correct Option is A
Solution and Explanation
Let's summarize the key deductions and conclusions made in the given information:
Total Dance Items: There are a total of 8 dance items.
First and Last Performances: The first performance was by Princess, composed by Badal, and the last performance was by Rani, composed by Gagan.
Performance Sequencing Rule: No dancer performed her second item before the performance of the first item by all the other dancers, and the dancers performed their second item in the same sequence as their first.
Compositions by Ashman: Ashman composed the fourth and fifth performances, as the first four performances were by four different composers.
Composer Assignments: If the sixth performance was composed by Badal, then the seventh would have been composed by Dyu. However, this leads to an inconsistency. Thus, the second, third, sixth, and seventh performances were composed by Dyu, Gagan, Badal, and Dyu, respectively.
Remaining Compositions: The remaining compositions (1, 8) are assigned to Ashman. The overall sequence is as follows:
- First: Princess, Badal
- Second: Samragni, Dyu
- Third: Queen, Gagan
- Fourth: Rani, Ashman
- Fifth: Rani, Ashman
- Sixth: Samragni, Badal
- Seventh: Queen, Dyu
- Eighth: Princess, Ashman
The 1st and 6th performances were composed by the same composer. Answer: (The first and the sixth)
Top Questions on Conclusion
- 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. - Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam.
The following facts are known about these ten musicians.
1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla.
2. D is an expert in both tabla and ghatam.
3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam.
4. Neither I nor J is an expert in tabla.
5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam. - A large store has only three departments, Clothing, Produce, and Electronics. The following figure shows the percentages of revenue and cost from the three departments for the years 2016, 2017 and 2018. The dotted lines depict percentage levels. So for example, in 2016, 50% of store's revenue came from its Electronics department while 40% of its costs were incurred in the Produce department.
In this setup, Profit is computed as (Revenue – Cost) and Percentage Profit as Profit/Cost × 100%.
It is known that
1. The percentage profit for the store in 2016 was 100%.
2. The store’s revenue doubled from 2016 to 2017, and its cost doubled from 2016 to 2018.
3. There was no profit from the Electronics department in 2017.
4. In 2018, the revenue from the Clothing department was the same as the cost incurred in the Produce department.
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been
- CAT - 2024
- Time and Work
- Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Profit and Loss
- Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
- CAT - 2024
- Time and Work
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems