The following additional facts are known.
1. A and B are to be placed in consecutively numbered shelves in increasing order
2. I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.
3. D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.
4. K is to be placed in shelf number 16.
5. L and J are items of the same type, while H is an item of a different type.
6. C is a candy and is to be placed in a shelf preceded by two empty shelves.
7. L is to be placed in a shelf preceded by exactly one empty shelf.
In how many different ways can the items be arranged on the shelves?
- 2
- 8
- 4
- 1
The Correct Option is B
Solution and Explanation
There are a total of 12 items, consisting of 5 biscuits, 3 candies, and 4 savories. The information specifies that item K is located on shelf 16. Items D, E, and F occupy consecutively numbered shelves in ascending order and are positioned after biscuits and candies. Consequently, D, E, F, and K are placed in shelves numbered 13, 14, 15, and 16, respectively.
Now, items L and J belong to the same category. Since I and J are on consecutively numbered shelves, it can be concluded that L, I, and J are either biscuits or candies. Given that C is a candy, if L, I, and J were candies, there would be a total of four candies, which is not feasible as there are only three. Therefore, L, I, and J are biscuits. As H differs from L, H must be a candy. Both A and B are on consecutively numbered shelves, indicating they are of the same type. If A and B were candies, the total number of candies would be four, contradicting the provided information that there are only three candies. Consequently, A and B are biscuits.
Two cases are considered:
Case 1: Candies are placed after biscuits
- L is placed after exactly one empty shelf, indicating L is in shelf 2.
- Shelves 2, 3, 4, 5, and 6 contain biscuits.
- A and B are in shelves 3 and 4 (biscuits).
- I and J are in shelves 5 and 6 (biscuits).
- C is in shelf 9.
- G and H are in shelves 10 and 11.
- Shelf 12 is empty.
- Shelves 1, 7, 8, and 12 are empty.
| Biscuits | 2. L 3.A 4. B 5.1/J 6. J/l |
| Candies | 9. C 10.H/G 11.G/H |
| Savories | 13.D 14.E 15.F 16.K |
Case 2: Biscuits are placed after candies.
- C is in shelf 3 (candy).
- G and H are in shelves 4 and 5.
- Shelf 6 is empty.
- L is in shelf 7.
- Shelves 7, 8, 9, 10, and 11 have biscuits.
- A and B are in shelves 8 and 9 (biscuits).
- I and J are in shelves 10 and 11 (biscuits).
- Shelf 12 is empty.
- Shelves 1, 2, 6, and 12 are empty.
| Candies | 3. C 4. H/G 5. G/H |
| Biscuits | 7. L 8. A 9. B 10. I/J 11. J/l |
| Savories | 13. D 14. E 15. F 16. K |
In the first scenario, there are four possible arrangements, and in the second scenario, there are also four possible arrangements. Consequently, there are a total of eight ways in which the items can be arranged. Answer: (8)
Which of the following items is not a type of biscuit?
- G
- B
- L
- A
The Correct Option is A
Solution and Explanation
There are a total of 12 items, consisting of 5 biscuits, 3 candies, and 4 savories. The information specifies that item K is located on shelf 16. Items D, E, and F occupy consecutively numbered shelves in ascending order and are positioned after biscuits and candies. Consequently, D, E, F, and K are placed in shelves numbered 13, 14, 15, and 16, respectively.
Now, items L and J belong to the same category. Since I and J are on consecutively numbered shelves, it can be concluded that L, I, and J are either biscuits or candies. Given that C is a candy, if L, I, and J were candies, there would be a total of four candies, which is not feasible as there are only three. Therefore, L, I, and J are biscuits. As H differs from L, H must be a candy. Both A and B are on consecutively numbered shelves, indicating they are of the same type. If A and B were candies, the total number of candies would be four, contradicting the provided information that there are only three candies. Consequently, A and B are biscuits.
Two cases are considered:
Case 1: Candies are placed after biscuits
- L is placed after exactly one empty shelf, indicating L is in shelf 2.
- Shelves 2, 3, 4, 5, and 6 contain biscuits.
- A and B are in shelves 3 and 4 (biscuits).
- I and J are in shelves 5 and 6 (biscuits).
- C is in shelf 9.
- G and H are in shelves 10 and 11.
- Shelf 12 is empty.
- Shelves 1, 7, 8, and 12 are empty.
| Biscuits | 2. L 3.A 4. B 5.1/J 6. J/l |
| Candies | 9. C 10.H/G 11.G/H |
| Savories | 13.D 14.E 15.F 16.K |
Case 2: Biscuits are placed after candies.
- C is in shelf 3 (candy).
- G and H are in shelves 4 and 5.
- Shelf 6 is empty.
- L is in shelf 7.
- Shelves 7, 8, 9, 10, and 11 have biscuits.
- A and B are in shelves 8 and 9 (biscuits).
- I and J are in shelves 10 and 11 (biscuits).
- Shelf 12 is empty.
- Shelves 1, 2, 6, and 12 are empty.
| Candies | 3. C 4. H/G 5. G/H |
| Biscuits | 7. L 8. A 9. B 10. I/J 11. J/l |
| Savories | 13. D 14. E 15. F 16. K |
G is not a biscuit. Answer: (G)
Which of the following can represent the numbers of the empty shelves in a possible arrangement?
- 1,7,11,12
- 1,5,6,12
- 1,2,6,12
- 1,2,8,12
The Correct Option is C
Solution and Explanation
There are a total of 12 items, consisting of 5 biscuits, 3 candies, and 4 savories. The information specifies that item K is located on shelf 16. Items D, E, and F occupy consecutively numbered shelves in ascending order and are positioned after biscuits and candies. Consequently, D, E, F, and K are placed in shelves numbered 13, 14, 15, and 16, respectively.
Now, items L and J belong to the same category. Since I and J are on consecutively numbered shelves, it can be concluded that L, I, and J are either biscuits or candies. Given that C is a candy, if L, I, and J were candies, there would be a total of four candies, which is not feasible as there are only three. Therefore, L, I, and J are biscuits. As H differs from L, H must be a candy. Both A and B are on consecutively numbered shelves, indicating they are of the same type. If A and B were candies, the total number of candies would be four, contradicting the provided information that there are only three candies. Consequently, A and B are biscuits.
Two cases are considered:
Case 1: Candies are placed after biscuits
- L is placed after exactly one empty shelf, indicating L is in shelf 2.
- Shelves 2, 3, 4, 5, and 6 contain biscuits.
- A and B are in shelves 3 and 4 (biscuits).
- I and J are in shelves 5 and 6 (biscuits).
- C is in shelf 9.
- G and H are in shelves 10 and 11.
- Shelf 12 is empty.
- Shelves 1, 7, 8, and 12 are empty.
| Biscuits | 2. L 3.A 4. B 5.1/J 6. J/l |
| Candies | 9. C 10.H/G 11.G/H |
| Savories | 13.D 14.E 15.F 16.K |
Case 2: Biscuits are placed after candies.
- C is in shelf 3 (candy).
- G and H are in shelves 4 and 5.
- Shelf 6 is empty.
- L is in shelf 7.
- Shelves 7, 8, 9, 10, and 11 have biscuits.
- A and B are in shelves 8 and 9 (biscuits).
- I and J are in shelves 10 and 11 (biscuits).
- Shelf 12 is empty.
- Shelves 1, 2, 6, and 12 are empty.
| Candies | 3. C 4. H/G 5. G/H |
| Biscuits | 7. L 8. A 9. B 10. I/J 11. J/l |
| Savories | 13. D 14. E 15. F 16. K |
Shelves numbered 1, 2, 6 and 12 can be empty. Answer: (1,2, 6. 12)
Which of the following statements is necessarily true?
- There are two empty shelves between the biscuits and the candies.
- All biscuits are kept before candies.
- There are at least four shelves between items B and C
- All candies are kept before biscuits.
The Correct Option is C
Solution and Explanation
There are a total of 12 items, consisting of 5 biscuits, 3 candies, and 4 savories. The information specifies that item K is located on shelf 16. Items D, E, and F occupy consecutively numbered shelves in ascending order and are positioned after biscuits and candies. Consequently, D, E, F, and K are placed in shelves numbered 13, 14, 15, and 16, respectively.
Now, items L and J belong to the same category. Since I and J are on consecutively numbered shelves, it can be concluded that L, I, and J are either biscuits or candies. Given that C is a candy, if L, I, and J were candies, there would be a total of four candies, which is not feasible as there are only three. Therefore, L, I, and J are biscuits. As H differs from L, H must be a candy. Both A and B are on consecutively numbered shelves, indicating they are of the same type. If A and B were candies, the total number of candies would be four, contradicting the provided information that there are only three candies. Consequently, A and B are biscuits.
Two cases are considered:
Case 1: Candies are placed after biscuits
- L is placed after exactly one empty shelf, indicating L is in shelf 2.
- Shelves 2, 3, 4, 5, and 6 contain biscuits.
- A and B are in shelves 3 and 4 (biscuits).
- I and J are in shelves 5 and 6 (biscuits).
- C is in shelf 9.
- G and H are in shelves 10 and 11.
- Shelf 12 is empty.
- Shelves 1, 7, 8, and 12 are empty.
| Biscuits | 2. L 3.A 4. B 5.1/J 6. J/l |
| Candies | 9. C 10.H/G 11.G/H |
| Savories | 13.D 14.E 15.F 16.K |
Case 2: Biscuits are placed after candies.
- C is in shelf 3 (candy).
- G and H are in shelves 4 and 5.
- Shelf 6 is empty.
- L is in shelf 7.
- Shelves 7, 8, 9, 10, and 11 have biscuits.
- A and B are in shelves 8 and 9 (biscuits).
- I and J are in shelves 10 and 11 (biscuits).
- Shelf 12 is empty.
- Shelves 1, 2, 6, and 12 are empty.
| Candies | 3. C 4. H/G 5. G/H |
| Biscuits | 7. L 8. A 9. B 10. I/J 11. J/l |
| Savories | 13. D 14. E 15. F 16. K |
There is a minimum of four shelves between B and C in both situations. This statement is correct. Answer: (There are at least four shelves between items B and C.)
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.
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