# CAT 2023 Question Paper DILR Slot 1

Instructions

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 forĀ UK applications, Schengen applications and Others applications. Applicants are called inĀ for processing sequentially on a first-come-first-served basis whenever a counter getsĀ freed for their category. The processing time for an application is the same within eachĀ category. But it may vary across the categories. Each US and UK application requires 10Ā minutes of processing time. Depending on the number of applications in a category andĀ time required to process an application for that category, it is possible that an applicant forĀ a slot may be processed later.

On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing inĀ that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they enteredĀ the office, exactly six out of the ten counters were either processing applications, or hadĀ 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 inĀ the Others category.

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.

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Question 29

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

Instructions

The schematic diagram below shows 12 rectangular houses in a housing complex. HouseĀ numbers are mentioned in the rectangles representing the houses. The houses are located in six columns - Column-A through Column-F, and two rows - Row-1 and Row-2.Ā The houses are divided into two blocks - Block XX and Block YY. The diagram also showsĀ two roads, one passing in front of the houses in Row-2 and another between the twoĀ blocks.

Some of the houses are occupied. The remaining ones are vacant and are the only onesĀ available for sale.

The road adjacency value of a house is the number of its sides adjacent to a road. ForĀ example, the road adjacency values of C2, F2, and B1 are 2, 1, and 0, respectively. The neighbour count of a house is the number of sides of that house adjacent to occupiedĀ houses in the same block. For example, E1 and C1 can have the maximum possible neighbour counts of 3 and 2, respectively.

The base price of a vacant house is Rs. 10 lakhs if the house does not have a parkingĀ space, and Rs. 12 lakhs if it does. The quoted price (in lakhs of Rs.) of a vacant house isĀ calculated as (base price) + 5 Ć (road adjacency value) + 3 Ć (neighbour count).Ā The following information is also known.

1. The maximum quoted price of a house in Block XX is Rs. 24 lakhs. The minimumĀ quoted price of a house in block YY is Rs. 15 lakhs, and one such house is in Column-E.
2. Row-1 has two occupied houses, one in each block.
3. Both houses in Column-E are vacant. Each of Column-D and Column-F has at least oneĀ occupied house.
4. There is only one house with parking space in Block YY.

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Question 33

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Question 34

## Which house in Block YY has parking space?

Instructions

Five restaurants, coded R1, R2, R3, R4 and R5 gave integer ratings to five gig workers -

Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of 1 to 5.

The means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4Ā respectively.
The summary statistics of these ratings for the five workers is given below.

* Range of ratings is defined as the difference between the maximum and minimum ratingsĀ awarded to a worker.

The following is partial information about ratings of 1 and 5 awarded by the restaurants toĀ the workers.

(a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, andĀ R5 to Vasu.
(b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.

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Question 36

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Question 37

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Question 38

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Question 39

## Which among the following restaurants gave its median rating to exactly one of the workers?

Instructions

Faculty members in a management school can belong to one of four departments - Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively.

Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of theĀ school's faculty who were candidates for the post of the Dean of the school. Only one of theĀ candidates was from O&Q.

Every faculty member, including the four candidates, voted for the post. In each department,Ā all the faculty members who were not candidates voted for the same candidate. The rules forĀ the election are listed below.

1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.

After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi receivedĀ 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. PakrasiĀ voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof.Ā Qureshi and Prof. Samuel for Prof. Pakrasi.

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