There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.
1. All slots were full.
2. The number of US applications was the same in all the slots. The same was true for the other three categories.
3. 50% of the applications were US applications.
4. All applicants except Ira, Vijay and Nandini arrived on time.
5. Vijay was called to a counter at 9:25 am.
How many UK applications were scheduled on that day?
Solution and Explanation
Applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
So, the total number of applicants is 200 (20 slots * 10 applications per slot).
50% of the applications are from the US, and the number of US applications is the same in each slot. The same applies to the other three categories.
So, the total number of US applicants is 100 (200 * 50%), and the number of US applicants in each slot is 5 (100 / 20).
Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at the 9:15 am slot. Since the number of Schengen applicants is the same in each slot, there must be at least 3 Schengen applicants per slot.
Mahira and Osman were scheduled in the 9:30 am slot for visa processing in the Others category, so there are at least 2 applicants in the Others category per slot.
Since there are 10 applicants per slot, and we already have 3 Schengen and 2 Others applicants, there are no UK applicants in each slot.
There are 10 counters in total, with 4 dedicated to US applications and 2 each for UK, Schengen, and Others. Each US and UK application takes 10 minutes to process. Vijay, who was 5th in the queue, was called to a counter at 9:25 am. This implies that the processing time for Schengen applications is 12.5 minutes.
| US (10 min) | schengen(12.5 min) | Others (5 min process) | |||||
| End Time | End Time | End Time | |||||
| C1 | C2 | C3 | C4 | C1 | C2 | C1 | C2 |
| 9.10 | 9.10 | 9.10 | 9.10 | 9.12.30 | 9.12.30 | 9.05 | 9.05 |
| 9.20 | 9.25 | 9.25 | 9.25 | 9.25 | 9.32.30 | 9.20 | 9.20 |
| 9.30 | 9.35 | 9.40 | 9.40 | 9.37.30 | 9.45 | 9.35 | 9.35 |
| 9.40 | 9.45 | 9.50 | 9.55 | ||||
| 9.55 | 9.55 | 10.00 | 10.05 | ||||
| 10.10 | 10.10 | 10.10 | 10.15 | ||||
| 10.20 | |||||||
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at 9:15 am but entered the VPO at 9:20 am. When they entered, 6 out of the 10 counters were processing applications or had just finished and were ready to start new ones. Thus, there were 4 free counters: 2 UK and 2 Others (since the US and Schengen counters were busy or had just finished processing).
From the table, the number of UK applicants in each slot is zero, so the total number of UK applicants is zero.
What is the maximum possible value of the total time (in minutes, nearest to its integer value) required to process all applications in the Others category on that day?
Solution and Explanation
Applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
So, the total number of applicants is 200 (20 slots * 10 applications per slot).
50% of the applications are from the US, and the number of US applications is the same in each slot. The same applies to the other three categories.
So, the total number of US applicants is 100 (200 * 50%), and the number of US applicants in each slot is 5 (100 / 20).
Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at the 9:15 am slot. Since the number of Schengen applicants is the same in each slot, there must be at least 3 Schengen applicants per slot.
Mahira and Osman were scheduled in the 9:30 am slot for visa processing in the Others category, so there are at least 2 applicants in the Others category per slot.
Since there are 10 applicants per slot, and we already have 3 Schengen and 2 Others applicants, there are no UK applicants in each slot.
There are 10 counters in total, with 4 dedicated to US applications and 2 each for UK, Schengen, and Others. Each US and UK application takes 10 minutes to process. Vijay, who was 5th in the queue, was called to a counter at 9:25 am. This implies that the processing time for Schengen applications is 12.5 minutes.
| US (10 min) | schengen(12.5 min) | Others (5 min process) | |||||
| End Time | End Time | End Time | |||||
| C1 | C2 | C3 | C4 | C1 | C2 | C1 | C2 |
| 9.10 | 9.10 | 9.10 | 9.10 | 9.12.30 | 9.12.30 | 9.05 | 9.05 |
| 9.20 | 9.25 | 9.25 | 9.25 | 9.25 | 9.32.30 | 9.20 | 9.20 |
| 9.30 | 9.35 | 9.40 | 9.40 | 9.37.30 | 9.45 | 9.35 | 9.35 |
| 9.40 | 9.45 | 9.50 | 9.55 | ||||
| 9.55 | 9.55 | 10.00 | 10.05 | ||||
| 10.10 | 10.10 | 10.10 | 10.15 | ||||
| 10.20 | |||||||
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at 9:15 am but entered the VPO at 9:20 am. When they entered, 6 out of the 10 counters were processing applications or had just finished and were ready to start new ones. Thus, there were 4 free counters: 2 UK and 2 Others (since the US and Schengen counters were busy or had just finished processing).
For the other category of applicants, the time taken to process one application is at most 5 minutes. This means the total time taken to process 40 applications is at most 200 minutes (40 applications * 5 minutes per application).
Which of the following is the closest to the time when Nandini's application process got over?
- 9: 45am
- 9: 50am
- 9: 35am
- 9: 37am
The Correct Option is A
Solution and Explanation
Applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
So, the total number of applicants is 200 (20 slots * 10 applications per slot).
50% of the applications are from the US, and the number of US applications is the same in each slot. The same applies to the other three categories.
So, the total number of US applicants is 100 (200 * 50%), and the number of US applicants in each slot is 5 (100 / 20).
Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at the 9:15 am slot. Since the number of Schengen applicants is the same in each slot, there must be at least 3 Schengen applicants per slot.
Mahira and Osman were scheduled in the 9:30 am slot for visa processing in the Others category, so there are at least 2 applicants in the Others category per slot.
Since there are 10 applicants per slot, and we already have 3 Schengen and 2 Others applicants, there are no UK applicants in each slot.
There are 10 counters in total, with 4 dedicated to US applications and 2 each for UK, Schengen, and Others. Each US and UK application takes 10 minutes to process. Vijay, who was 5th in the queue, was called to a counter at 9:25 am. This implies that the processing time for Schengen applications is 12.5 minutes.
| US (10 min) | schengen(12.5 min) | Others (5 min process) | |||||
| End Time | End Time | End Time | |||||
| C1 | C2 | C3 | C4 | C1 | C2 | C1 | C2 |
| 9.10 | 9.10 | 9.10 | 9.10 | 9.12.30 | 9.12.30 | 9.05 | 9.05 |
| 9.20 | 9.25 | 9.25 | 9.25 | 9.25 | 9.32.30 | 9.20 | 9.20 |
| 9.30 | 9.35 | 9.40 | 9.40 | 9.37.30 | 9.45 | 9.35 | 9.35 |
| 9.40 | 9.45 | 9.50 | 9.55 | ||||
| 9.55 | 9.55 | 10.00 | 10.05 | ||||
| 10.10 | 10.10 | 10.10 | 10.15 | ||||
| 10.20 | |||||||
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at 9:15 am but entered the VPO at 9:20 am. When they entered, 6 out of the 10 counters were processing applications or had just finished and were ready to start new ones. Thus, there were 4 free counters: 2 UK and 2 Others (since the US and Schengen counters were busy or had just finished processing).
Nandini's position was sixth in the queue for Schengen applications. According to the table, her processing will end at 9:45 am.
Which of the following statements is false?
- The application process of Osman was completed before 9:45 am
- The application process of Mahira started after Nandini's.
- The application process of Mahira was completed before Nandini's.
- The application process of Osman was completed before Vijay's.
The Correct Option is B
Solution and Explanation
Applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
So, the total number of applicants is 200 (20 slots * 10 applications per slot).
50% of the applications are from the US, and the number of US applications is the same in each slot. The same applies to the other three categories.
So, the total number of US applicants is 100 (200 * 50%), and the number of US applicants in each slot is 5 (100 / 20).
Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at the 9:15 am slot. Since the number of Schengen applicants is the same in each slot, there must be at least 3 Schengen applicants per slot.
Mahira and Osman were scheduled in the 9:30 am slot for visa processing in the Others category, so there are at least 2 applicants in the Others category per slot.
Since there are 10 applicants per slot, and we already have 3 Schengen and 2 Others applicants, there are no UK applicants in each slot.
There are 10 counters in total, with 4 dedicated to US applications and 2 each for UK, Schengen, and Others. Each US and UK application takes 10 minutes to process. Vijay, who was 5th in the queue, was called to a counter at 9:25 am. This implies that the processing time for Schengen applications is 12.5 minutes.
| US (10 min) | schengen(12.5 min) | Others (5 min process) | |||||
| End Time | End Time | End Time | |||||
| C1 | C2 | C3 | C4 | C1 | C2 | C1 | C2 |
| 9.10 | 9.10 | 9.10 | 9.10 | 9.12.30 | 9.12.30 | 9.05 | 9.05 |
| 9.20 | 9.25 | 9.25 | 9.25 | 9.25 | 9.32.30 | 9.20 | 9.20 |
| 9.30 | 9.35 | 9.40 | 9.40 | 9.37.30 | 9.45 | 9.35 | 9.35 |
| 9.40 | 9.45 | 9.50 | 9.55 | ||||
| 9.55 | 9.55 | 10.00 | 10.05 | ||||
| 10.10 | 10.10 | 10.10 | 10.15 | ||||
| 10.20 | |||||||
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at 9:15 am but entered the VPO at 9:20 am. When they entered, 6 out of the 10 counters were processing applications or had just finished and were ready to start new ones. Thus, there were 4 free counters: 2 UK and 2 Others (since the US and Schengen counters were busy or had just finished processing).
Let's verify the options with the given information.
Option A: The application process of Osman was completed before 9:45 am.
- If Osman is 5th in the queue for his category and each application takes at most 5 minutes, his process would end by 9:35 am (starting at 9:30 am).
- True: Osman's application process ends before 9:45 am.
Option B: The application process of Mahira started after Nandini's.
- Mahira's application process starts at 9:30 am.
- Nandini's application process starts at 9:32:30 am (since she is 6th in the queue for Schengen applications and each takes 2.5 minutes, starting from 9:15 am).
- False: Mahira's process starts before Nandini's.
The correct answer is Option B.
When did the application processing for all US applicants get over on that day?
- 3 : 40 pm
- 2 : 00 pm
- 2: 25 pm
- 2 : 05 pm
The Correct Option is D
Solution and Explanation
Applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
So, the total number of applicants is 200 (20 slots * 10 applications per slot).
50% of the applications are from the US, and the number of US applications is the same in each slot. The same applies to the other three categories.
So, the total number of US applicants is 100 (200 * 50%), and the number of US applicants in each slot is 5 (100 / 20).
Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at the 9:15 am slot. Since the number of Schengen applicants is the same in each slot, there must be at least 3 Schengen applicants per slot.
Mahira and Osman were scheduled in the 9:30 am slot for visa processing in the Others category, so there are at least 2 applicants in the Others category per slot.
Since there are 10 applicants per slot, and we already have 3 Schengen and 2 Others applicants, there are no UK applicants in each slot.
There are 10 counters in total, with 4 dedicated to US applications and 2 each for UK, Schengen, and Others. Each US and UK application takes 10 minutes to process. Vijay, who was 5th in the queue, was called to a counter at 9:25 am. This implies that the processing time for Schengen applications is 12.5 minutes.
| US (10 min) | schengen(12.5 min) | Others (5 min process) | |||||
| End Time | End Time | End Time | |||||
| C1 | C2 | C3 | C4 | C1 | C2 | C1 | C2 |
| 9.10 | 9.10 | 9.10 | 9.10 | 9.12.30 | 9.12.30 | 9.05 | 9.05 |
| 9.20 | 9.25 | 9.25 | 9.25 | 9.25 | 9.32.30 | 9.20 | 9.20 |
| 9.30 | 9.35 | 9.40 | 9.40 | 9.37.30 | 9.45 | 9.35 | 9.35 |
| 9.40 | 9.45 | 9.50 | 9.55 | ||||
| 9.55 | 9.55 | 10.00 | 10.05 | ||||
| 10.10 | 10.10 | 10.10 | 10.15 | ||||
| 10.20 | |||||||
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order at 9:15 am but entered the VPO at 9:20 am. When they entered, 6 out of the 10 counters were processing applications or had just finished and were ready to start new ones. Thus, there were 4 free counters: 2 UK and 2 Others (since the US and Schengen counters were busy or had just finished processing).
Let's verify the details step by step.
The first slot takes 20 minutes to complete, and the remaining 19 slots each take 15 minutes to complete the US application process. Therefore, the total time taken is calculated as follows:
- First slot: 20 minutes
- Remaining 19 slots: 19 slots * 15 minutes = 285 minutes
Total time taken = 20 minutes + 285 minutes = 305 minutes
305 minutes is equal to 5 hours and 5 minutes.
Starting at 9:00 am, adding 5 hours and 5 minutes brings us to:
9:00 am + 5 hours = 2:00 pm 2:00 pm + 5 minutes = 2:05 pm
Therefore, the correct time is 2:05 pm.
Options Check:
Option A: The application process of Osman was completed before 9:45 am.
- We previously established that Osman's application process, starting at 9:30 am and being 5th in his category, ends at 9:35 am.
- True: Osman's process ends before 9:45 am.
Option B: The application process of Mahira started after Nandini's.
- Mahira's application process starts at 9:30 am.
- Nandini's application process starts at 9:32:30 am.
- False: Mahira's process starts before Nandini's.
Therefore, the correct option is indeed Option D.
Top Questions on Data Analysis
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The following additional information is known.
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