CAT 2023 Slot 1 — DILR Question 1

Mixed PracticeEasy

Passage / Data

Answer the following questions based on the information given below:

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?

Answer & solution

Answer: 0

Solution

Easy

This whole set rests on one decoding of the office. First nail down how many applications of each category sit in every slot, then read the timing facts. Once the composition is fixed, every question is a short look-up.

The fixed picture (used by all 5 questions). $20$ slots of $15$ min, $10$ applications per slot $\Rightarrow 200$ applications. US $=50\%\Rightarrow 5$ US per slot. The remaining $5$ per slot are split among UK, Schengen, Others (equal in every slot). Two named groups pin the split: the trio Ira–Vijay–Nandini are $3$ Schengen in one slot, and Mahira–Osman are $2$ Others in one slot.

Category	Counters	Per slot	Day total	Time/app
US	4	5	100	10 min
UK	2	0	0	10 min
Schengen	2	3	60	12.5 min
Others	2	2	40	$\le 5$ min

Fix the per-slot counts. US is $5$ per slot. With Schengen $\ge 3$ (the trio) and Others $\ge 2$ (Mahira, Osman), and only $5$ non-US places per slot:

\underbrace{3}_{\text{Sch}}+\underbrace{2}_{\text{Others}}=5\ \Rightarrow\ \text{UK}=0.

So the split per slot is exactly US $5$ , Schengen $3$ , Others $2$ , UK $0$ .

Read the question. It asks for the number of UK applications scheduled that day. UK has $0$ per slot, so the day total is $0\times 20 = 0$ .

\mathbf{0}\ \text{UK applications}