CAT — Resource Scheduling
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A visa processing office (VPO) accepts visa applications in four categories – US, UK, Schengen, and Others. The 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.
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?
Step 1:
The VPO operates for 20 time slots of 15 minutes each, from 9:00 AM to 2:00 PM, and has 10 counters.
From the given information and condition (1), the total number of applications scheduled is:
10 × 20 = 200
According to condition (3), there are 100 US visa applications.
Hence, the remaining 100 applications belong to the other three visa categories.
Using condition (2), the number of US visa applications per slot is:
100 ÷ 20 = 5
Similarly, the combined number of applications for the remaining three categories per slot is also:
100 ÷ 20 = 5
The processing time for each application is fixed within a category, although it may differ across categories.
Therefore, depending on the number of applications in a category and its processing time, an application assigned to a particular slot may actually be processed in a later slot.
The available information is:
- US: 4 counters, Processing time = 10 minutes
- UK: 2 counters, Processing time = 10 minutes
- Schengen: 2 counters, Processing time = Unknown
- Others: 2 counters, Processing time = Unknown
Step 2:
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order for the 9:15 AM slot. However, they entered the VPO at 9:20 AM, resulting in a 5-minute delay.
This implies that at least three applicants were scheduled for the Schengen category in each time slot.
Similarly, Mahira and Osman were scheduled for visa processing under the Others category in the 9:30 AM slot.
Therefore, at least two applicants were scheduled for the Others category in every time slot.
The total number of applications scheduled that day was 200.
Out of these, 100 were US visa applications.
Therefore, each 15-minute time slot had:
100 ÷ 20 = 5 US applications
From the previous deductions, each time slot also had:
- 3 Schengen applications
- 2 Others applications
Thus, all 10 application slots in each time slot are accounted for:
- US = 5
- Schengen = 3
- Others = 2
This leaves no applications for the UK category in any time slot.
Hence, the number of UK applications per time slot is 0.
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?
Step 1:
The VPO operates for 20 time slots of 15 minutes each, from 9:00 AM to 2:00 PM, and has 10 counters.
From the given information and condition (1), the total number of applications scheduled is:
10 × 20 = 200
According to condition (3), there are 100 US visa applications.
Hence, the remaining 100 applications belong to the other three visa categories.
Using condition (2), the number of US visa applications per slot is:
100 ÷ 20 = 5
Similarly, the combined number of applications for the remaining three categories per slot is also:
100 ÷ 20 = 5
The processing time for each application is fixed within a category, although it may differ across categories.
Therefore, depending on the number of applications in a category and its processing time, an application assigned to a particular slot may actually be processed in a later slot.
The available information is:
- US: 4 counters, Processing time = 10 minutes
- UK: 2 counters, Processing time = 10 minutes
- Schengen: 2 counters, Processing time = Unknown
- Others: 2 counters, Processing time = Unknown
Step 2:
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order for the 9:15 AM slot. However, they entered the VPO at 9:20 AM, resulting in a 5-minute delay.
This implies that at least three applicants were scheduled for the Schengen category in each time slot.
Similarly, Mahira and Osman were scheduled for visa processing under the Others category in the 9:30 AM slot.
Therefore, at least two applicants were scheduled for the Others category in every time slot.
The maximum processing time for the Others category is 5 minutes per application.
Since there are 2 Others applications in each time slot and 20 time slots in total, the total processing time is:
= 2 × 5 × 20
= 200 minutes.
Which of the following is the closest to the time when Nandini’s application process got over?
9:35 am
9:37 am
9:45 am
9:50 am
9:45 am
Step 1:
The VPO operates for 20 time slots of 15 minutes each, from 9:00 AM to 2:00 PM, and has 10 counters.
From the given information and condition (1), the total number of applications scheduled is:
10 × 20 = 200
According to condition (3), there are 100 US visa applications.
Hence, the remaining 100 applications belong to the other three visa categories.
Using condition (2), the number of US visa applications per slot is:
100 ÷ 20 = 5
Similarly, the combined number of applications for the remaining three categories per slot is also:
100 ÷ 20 = 5
The processing time for each application is fixed within a category, although it may differ across categories.
Therefore, depending on the number of applications in a category and its processing time, an application assigned to a particular slot may actually be processed in a later slot.
The available information is:
- US: 4 counters, Processing time = 10 minutes
- UK: 2 counters, Processing time = 10 minutes
- Schengen: 2 counters, Processing time = Unknown
- Others: 2 counters, Processing time = Unknown
Step 2:
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order for the 9:15 AM slot. However, they entered the VPO at 9:20 AM, resulting in a 5-minute delay.
This implies that at least three applicants were scheduled for the Schengen category in each time slot.
Similarly, Mahira and Osman were scheduled for visa processing under the Others category in the 9:30 AM slot.
Therefore, at least two applicants were scheduled for the Others category in every time slot.
Hence, 9:45 AM is the closest time at which Nandini's visa application processing would have been completed.
Which of the following statements is false?
The application process of Mahira was completed before Nandini’s.
The application process of Osman was completed before Vijay’s.
The application process of Mahira started after Nandini’s.
The application process of Osman was completed before 9:45 am.
The application process of Mahira started after Nandini’s.
Step 1:
The VPO operates for 20 time slots of 15 minutes each, from 9:00 AM to 2:00 PM, and has 10 counters.
From the given information and condition (1), the total number of applications scheduled is:
10 × 20 = 200
According to condition (3), there are 100 US visa applications.
Hence, the remaining 100 applications belong to the other three visa categories.
Using condition (2), the number of US visa applications per slot is:
100 ÷ 20 = 5
Similarly, the combined number of applications for the remaining three categories per slot is also:
100 ÷ 20 = 5
The processing time for each application is fixed within a category, although it may differ across categories.
Therefore, depending on the number of applications in a category and its processing time, an application assigned to a particular slot may actually be processed in a later slot.
The available information is:
- US: 4 counters, Processing time = 10 minutes
- UK: 2 counters, Processing time = 10 minutes
- Schengen: 2 counters, Processing time = Unknown
- Others: 2 counters, Processing time = Unknown
Step 2:
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order for the 9:15 AM slot. However, they entered the VPO at 9:20 AM, resulting in a 5-minute delay.
This implies that at least three applicants were scheduled for the Schengen category in each time slot.
Similarly, Mahira and Osman were scheduled for visa processing under the Others category in the 9:30 AM slot.
Therefore, at least two applicants were scheduled for the Others category in every time slot.
When did the application processing for all US applicants get over on that day?
2:00 pm
2:05 pm
2:25 pm
3:40 pm
2:05 pm
Step 1:
The VPO operates for 20 time slots of 15 minutes each, from 9:00 AM to 2:00 PM, and has 10 counters.
From the given information and condition (1), the total number of applications scheduled is:
10 × 20 = 200
According to condition (3), there are 100 US visa applications.
Hence, the remaining 100 applications belong to the other three visa categories.
Using condition (2), the number of US visa applications per slot is:
100 ÷ 20 = 5
Similarly, the combined number of applications for the remaining three categories per slot is also:
100 ÷ 20 = 5
The processing time for each application is fixed within a category, although it may differ across categories.
Therefore, depending on the number of applications in a category and its processing time, an application assigned to a particular slot may actually be processed in a later slot.
The available information is:
- US: 4 counters, Processing time = 10 minutes
- UK: 2 counters, Processing time = 10 minutes
- Schengen: 2 counters, Processing time = Unknown
- Others: 2 counters, Processing time = Unknown
Step 2:
On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order for the 9:15 AM slot. However, they entered the VPO at 9:20 AM, resulting in a 5-minute delay.
This implies that at least three applicants were scheduled for the Schengen category in each time slot.
Similarly, Mahira and Osman were scheduled for visa processing under the Others category in the 9:30 AM slot.
Therefore, at least two applicants were scheduled for the Others category in every time slot.
The first five US applications require 20 minutes to be processed.
Thereafter, each subsequent batch of five applications is completed in 15 minutes.
Hence, the total time required to process all 100 US applications is:
= 20 + (15 × 19)
= 305 minutes
Therefore, the processing of all US visa applications on that day would be completed at 2:05 PM.
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