Previous Year CAT LR Questions

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Previous Year CAT LR Questions
Previous Year CAT LR Questions

Previous Year CAT LR Questions:

We have provided some Logical reasoning questions and answers from previous year question papers. These LR problems will help you to solve other logical reasoning questions. Detailed solutions are provided for the LR Questions below.

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Instructions: 1 to 4

Healthy Bites is a fastfood loint serving three items, burgers, fnes and ice cream. It has two employees Anish and Bani who prepare the items ordered by the clients. Preparation time is 10 minutes for a burger and 2 minutes for an order of Ice cream. An employee can prepare only one of these items at a time. The fries are prepared in an automatic fryer which can prepare upto to 3 portions of fries at a time, and takes 5 minutes irrespective of the number of portions. The fryer does not need an employee to constantly attend to it, and we can ignore the time taken by an employee to start and stop the fryer; thus, an employee can be engaged in preparing other items while the frying is on. However fries cannot be prepared in anticipation of future orders.

Healthy Bites wishes to serve the orders as early as possible. The individual items in any order are served as and when ready; however,the order is considered to be completely served only when all the items of that order are served.

The table below gives the orders of three clients and the times at which they placed their orders:


Question 1:Assume that only one client’s order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 1 completely served?a) 10:17
b) 10:10
c) 10:15
d) 10:20

Question 2:
Assume that only one client’s order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 3 completely served?a) 10:35
b) 10:22
c) 10:25
d) 10:17

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Question 3:
Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
At what time is the order placed by Client 2 completely served?

a) 10:10
b) 10:12
c) 10:15
d) 10:17

Question 4:

Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
Also assume that the fourth client came in only at 10:35. Between 10:00 and 10:30, for how many minutes is exactly one of the employees idle?

a) 7
b) 10
c) 15
d) 23

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Solutions (1 to 4)

1) Answer (b)

It is given that
1 burger takes 10 minutes
1 ice cream takes 2 minutes and 3 portions of fries take 5 min by the machine (operator is not required).
Client 1 ordered 1 burger, 3 portions of fries and 1 ice cream.
The burger will take 10 minutes to finish. Meantime, rest of the order can be completed.

2) Answer (c)

It is given that
1 burger takes 10 minutes
1 ice cream takes 2 minutes and 3 portions of fries take 5 min by the machine (operator is not required).
Anish or Bani cannot start preparing a new order while a previous order is being prepared.
The first order will be completely done at 10:10.
The second order is two fries and one ice cream, which will be done by 10:15.
The third order is one 1 burger and 1 portion of fries.
The burger will take 10 minutes, by which fries will be ready.
Thus, the third order will be completed by 10:25.

3) Answer (a)

It is given that
1 burger takes 10 minutes
1 ice cream takes 2 minutes and 3 portions of fries take 5 min by the machine (operator is not required).
The employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
The first order is 1 burger, 1 ice cream and 3 portions of fries.
Anish can start working on the burger and Bani can start working on the ice cream.
The burger will be done at 10:10, ice – cream at 10:02 and fries at 10:05.
The second order is placed at 10:05. (ice cream and fries)
Bani can work on the ice cream from 10:05 and also put the fries.
The ice cream will be done by 10:07 but the fries will be done by 10:10. Thus, order will be completed by 10:10.

4) Answer (b)

It is given that
1 burger takes 10 minutes
1 ice cream takes 2 minutes and 3 portions of fries take 5 min by the machine (operator is not required).
The employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
The first order is 1 burger, 1 ice cream and 3 portions of fries.
Anish can start working on the burger and Bani can start working on the ice cream.
The burger will be done at 10:10, ice – cream at 10:02 and fries at 10:05.
The second order is placed at 10:05. (ice cream and fries)
Bani can work on the ice cream from 10:05 and also put the fries.
Only Bani will be free from 10:02 to 10:05 – 3 minutes.
The ice cream will be done by 10:07 but the fries will be done by 10:10.
Third order of 1 burger and 1 fries is placed at 10:07.
Bani will immediately start working on the burger. He will finish it by 10:17.
Anish would have finished the first burger at 10:10. Only he is free till 10:17 – 7 minutes.
Thus exactly one person is free for 10 minutes.

Instructions: (5 to 8)

A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.
The underlying principle that they are working on is the following:
Any person staying in any of these lO cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.

Question 5:

If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is:

a) 45
b) 90
c) 180
d) 135

Question 6:

Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and liar terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is:

a) 54
b) 120
c) 96
d) 60

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Question 7:
Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
1. Both cities are in G1
2. Between A and any city in G2
3. Between B and any city in G3
4. Between C and any city in G4
Then the minimum number of direct flights that satisfies the underlying principle of the airline is:
Answer: 40
Solution : Number of flights between the cities of G1 = 3c2*4 = 12
Between cities in A and cities in G2 = 3*4 = 12
Between B and cities in G3 = 2*4 = 8
Between C and cities in G4 = 2*4 = 8
Total = 12*2 + 8*2 = 40

 

Question 8:
Suppose the 10 cities are divided into 4 distinct groups Gl, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that Gl consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
1. Both cities are in G1
2. Between A and any city in G2
3. Between B and any city in G3
4. Between C and any city in G4
However, due to operational difficulties at A, it was later decided that the only flights that would operate at A would be those to and from B. Cities in G2 would have to be assigned to G3 or to G4.
What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose?Answer: 4

Solution:  Let us determine the number of flights under new conditions.
Flights between A and B = 4
Between  B and any city in G3 = 4*4 = 16
Between C and any city in G4 = 4*4 = 16
Hence, total flights = 36
Thus, reduction = 40 – 36 = 4.

Solutions : for (5 and 6 )

5) Answer (c)

There are ten cities. We need to find the minimum number of flights required to travel from any city to any city. Any two cities can be selected in 10C2 ways. Now for these two cities, a person will need minimum 4 flights. (1 to go from A to B, 1 to go from B to A. Similarly, 1 to return to A and 1 to return to B) Thus, minimum number of required flights = 45*4 = 180.

6) Answer (c)

There are three hubs in total. Each city is connected to every other city via a hub. The total number of flights between the three hubs will be 3c2*4 = 12.
From each hub, there will be flights to 7 cities. So total total number of flights originating or terminating at each hub = 7*4 = 28. For all three hubs, it would be 28*3 = 84
Hence, the required number will be 84 + 12 = 96.

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