CAT 2023 Slot 1 DILR Set 3 Q11–Q15

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2023 Slot 1, with 5 questions (Scheduling). Answers are CAT's official key.

The set

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.

Question 11

How many UK applications were scheduled on that day?

TITA: type in the answer. There are no options and no negative marking.

Answer: 0 Scheduling TITA

Solution

  1. 200 applications, 10 per slot, 5 US per slot. Ira, Vijay, Nandini need at least 3 Schengen per slot and Mahira, Osman at least 2 Others, leaving 0 UK.
  2. With 3 Schengen and 2 Others per slot, \(5 - 3 - 2 = 0\) UK applications per slot, so 0 for the day. This also matches the count at 9:20: 4 US counters plus 2 Schengen counters are active, the UK counters idle.

Question 12

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?

TITA: type in the answer. There are no options and no negative marking.

Answer: 200 Scheduling TITA

Solution

  1. 200 applications, 10 per slot, 5 US per slot. Ira, Vijay, Nandini need at least 3 Schengen per slot and Mahira, Osman at least 2 Others, leaving 0 UK.
  2. Vijay called at 9:25 although he arrived at 9:20: one Schengen counter was still busy with the 9:00 slot's third applicant, who started at \(t\) and finished at \(2t = 25\), so a Schengen application takes 12.5 min. At 9:20 the 6 active counters are 4 US + 2 Schengen, so the Others counters had finished the 9:15 slot: Others take under 5 min.
  3. There are \(2\times20 = 40\) Others applications, each taking just under 5 minutes.
  4. Total processing time is just under \(40\times5 = 200\) minutes, i.e. 200 to the nearest integer.

Question 13

Which of the following is the closest to the time when Nandini's application process got over?
  1. A
    9:35 am
  2. B
    9:50 am
  3. C
    9:37 am
  4. D
    9:45 am

Answer: (D) 9:45 am Scheduling MCQ

Solution

  1. Vijay called at 9:25 although he arrived at 9:20: one Schengen counter was still busy with the 9:00 slot's third applicant, who started at \(t\) and finished at \(2t = 25\), so a Schengen application takes 12.5 min. At 9:20 the 6 active counters are 4 US + 2 Schengen, so the Others counters had finished the 9:15 slot: Others take under 5 min.
  2. Ira: 9:20 to 9:32.5; Vijay: 9:25 to 9:37.5.
  3. Nandini (who arrived before the 9:30 slot's applicants) takes the counter freed at 9:32.5 and finishes at 9:45.

Question 14

Which of the following statements is false?
  1. A
    The application process of Mahira was completed before Nandini's.
  2. B
    The application process of Osman was completed before Vijay's.
  3. C
    The application process of Osman was completed before 9:45 am.
  4. D
    The application process of Mahira started after Nandini's.

Answer: (D) The application process of Mahira started after Nandini's. Scheduling MCQ

Solution

  1. Vijay called at 9:25 although he arrived at 9:20: one Schengen counter was still busy with the 9:00 slot's third applicant, who started at \(t\) and finished at \(2t = 25\), so a Schengen application takes 12.5 min. At 9:20 the 6 active counters are 4 US + 2 Schengen, so the Others counters had finished the 9:15 slot: Others take under 5 min.
  2. Mahira and Osman (9:30 slot, Others) start at 9:30 and finish before 9:35. Nandini runs 9:32.5 to 9:45, Vijay finishes at 9:37.5.
  3. A, B, C are true. D is false: Mahira started at 9:30, before Nandini's 9:32.5.

Question 15

When did the application processing for all US applicants get over on that day?
  1. A
    2:25 pm
  2. B
    3:40 pm
  3. C
    2:00 pm
  4. D
    2:05 pm

Answer: (D) 2:05 pm Scheduling MCQ

Solution

  1. Each slot has 5 US applications, 4 counters, 10 minutes each. Slot 9:00: four run 9:00-9:10, the fifth 9:10-9:20.
  2. Slot 9:15: three counters are free (9:15-9:25), the fourth frees at 9:20 (9:20-9:30), and the fifth applicant gets a counter at 9:25 (9:25-9:35). So each slot's last applicant finishes 20 minutes after the slot begins, and no backlog builds up.
  3. The last slot starts at 1:45 pm, so US processing ends at 1:45 + 20 min = 2:05 pm.

Shortcut. 4 counters handle 6 applications per 15 min, more than the 5 that arrive, so only the last slot matters: 1:45 + 20 min.

Same concept in other years

See every question on Queue simulation: arrivals served by counters/rides/doctors in time slots.

More Scheduling questions from CAT

All 41 Scheduling questions asked since 2017.