CAT 2023 Slot 1 · DILR · Question 5

CAT 2023 Slot 1 previous year question on Caselet DI, with the answer and a step-by-step solution.

Caselet DIData InterpretationMultiple choiceMedium

Set 1: Visa Processing Office Schedule — this question belongs to a set. Read the full set with all 5 questions →

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.

When did the application processing for all US applicants get over on that day?

A
2:05 pm
B
2:25 pm
C
2:00 pm
D
3:40 pm

Pick an option, then check.

Answer & solution

Answer: Option A

Solving the set

Step 1 – Applications per slot. 20 slots × 10 = 200 applications. 50% are US, so 100 US, i.e., 5 per slot (every slot has the same mix).

The other 5 per slot: Ira, Vijay and Nandini are all Schengen in the 9:15 slot, so at least 3 Schengen per slot; Mahira and Osman are both Others in the 9:30 slot, so at least 2 Others per slot. 3 + 2 = 5 leaves nothing for UK.

Category	Per slot	Reason	Total for the day (20 slots)
US	5	50% of 10	100
Schengen	3	Ira, Vijay, Nandini share a slot (at least 3)	60
Others	2	Mahira, Osman share a slot (at least 2)	40
UK	0	10 − 5 − 3 − 2	0
Total	10		200

Step 2 – Schengen processing time (t). In the 9:00 slot, two Schengen applicants start at 9:00 and finish at 9:00 + t; the third starts at 9:00 + t and finishes at 9:00 + 2t. Ira arrives at 9:20.

• If t ≤ 20, a counter is free by 9:20 and Ira is called at 9:20. Vijay is called when the other counter frees, at 9:00 + 2t = 9:25, so t = 12.5 minutes.

• If t > 20, nobody is free at 9:20; Ira and the third 9:00 applicant would both start at 9:00 + t, and Vijay could not start before 9:00 + 2t > 9:40. Not possible.

So each Schengen application takes 12.5 minutes:

Schengen counter	Applicant	Start	End
Counter 1	9:00 slot – 1st	9:00	9:12:30
Counter 2	9:00 slot – 2nd	9:00	9:12:30
Counter 1	9:00 slot – 3rd	9:12:30	9:25
Counter 2	Ira	9:20	9:32:30
Counter 1	Vijay	9:25	9:37:30
Counter 2	Nandini	9:32:30	9:45

Step 3 – Others processing time. At 9:20 exactly six counters were active:

Counters	Status at 9:20 am	Counted
4 US	Busy (US queue never empties)	4
2 UK	No UK applications at all	0
2 Schengen	One processing the 3rd 9:00 applicant, one starting Ira	2
2 Others	Must be idle	0
Total		6

So the two Others counters were idle at 9:20: the two 9:15 Others applicants (started at 9:15) had finished by 9:20. Each Others application therefore takes at most 5 minutes.

Others applicant	Counter	Start	End (processing time t ≤ 5 min)
9:15 slot – 1st	1	9:15	by 9:20
9:15 slot – 2nd	2	9:15	by 9:20
Mahira	1	9:30	by 9:35
Osman	2	9:30	by 9:35

Step 4 – US counters. 5 US applicants arrive every 15 minutes for 4 counters of 10 minutes each.

Slot	Start times of its 5 US applicants	Last one ends
9:00	9:00, 9:00, 9:00, 9:00, 9:10	9:20
9:15	9:15, 9:15, 9:15, 9:20, 9:25	9:35
9:30	9:30, 9:30, 9:30, 9:35, 9:40	9:50
…	same pattern every slot	slot time + 20 min
1:45 pm (last)	1:45, 1:45, 1:45, 1:50, 1:55	2:05 pm

This question

From Step 4, the last US applicant of every slot (from 9:15 on) finishes 20 minutes after the slot time. The last slot is 1:45 pm, so all US processing ends at 2:05 pm.

Hence, the answer is option 1.

CAT 2023 Slot 1 · DILR · Question 5

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