CAT Exam Model Paper 2025, Mapping and Best Routes Questions - Day 57

On Day 57 of your CAT 2025 prep journey, it’s time to shift gears and focus on full-length practice. Solving model papers today will help you boost your speed, sharpen your accuracy, and manage your time better. You’ll tackle Para Summary in VARC, Logical Deductions and Connections in Logical Reasoning and some challenging Quant problems. These sets let you experience real exam-like situations and build a clear problem-solving approach. To keep your prep consistent, don’t forget to download the latest CAT sample papers in PDF format, they’re designed to match the updated exam pattern.

This Story also Contains

1. CAT Preparation 2025 in 60 Days
2. Strategies to Ace Route Questions in CAT 2025
3. CAT 2025 Ebooks by Careers360

CAT Preparation 2025 in 60 Days

CAT Preparation 2025 in 60 Days is possible with the right strategy, dedication, and smart resources. Follow our expert-designed 60-day CAT study plan to cover the complete CAT syllabus 2025, including CAT VARC, CAT DILR, and CAT Quantitative Aptitude. Use daily CAT practice sets, mock tests, and CAT sample papers to improve speed, accuracy, and overall exam performance effectively.

Part-1: Quantitative Aptitude for CAT Exam

CAT Exam Important Topic: Strategy through CAT Previous Year's Questions (CAT exam model paper) to prepare for quantitative aptitude for the CAT exam 2025

CAT Previous Years Questions from Quantitative Aptitude:

CAT previous years' question papers with solutions from quantitative aptitude are given below. CAT previous years question paper pdf free download is available and can be downloaded by clicking at the top of the page. This CAT exam model paper consists of questions from previous years including TITA (type in the answer).

Q1. Points E, F, G, and H lie respectively on the sides AB, BC, CD, and DA of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of the length of EB to that of CG is [CAT 2018, Geometry, Moderate]

1. 2: 5

2. 4: 9

3. 1: 3

4. 3: 8

Ans: [3]

Tip 1: Draw a rough diagram

Tip 2: Use Pythagoras' theorem to find the side of the internal square.

If the side of the ABCD is ‘a, then take the measurements as shown in the figure.

GF2 = GC2 + GF2

GF2 = (a-x)2 + x2

GF2 = a2 + x2 – 2ax + x2

GF2 = a2 + 2x2 – 2ax

Tip 3: Take the ratio areas of squares

Ar(ABCD)/Ar(EFGH) = 100/62.5 = 8/5

So, a2/ (a2 + 2x2 – 2ax) = 8/5

⇒ 5a2= 8(a2 + 2x2 – 2ax)

⇒ 16x2 +3a2 – 16ax= 0

On solving, we get x = a/4 or x = 3a/4

EB < CG, so x must be a/4 and CG = 3a/4

So, EB/CG = (a/4)/(3a/4) = 1: 3

Q.2

[CAT 2019, Moderate, Logarithm]

1. 2: 5

2. 4: 9

3. 1: 3

4. 3: 8

Ans: [3]

CAT Tips: In such questions, logarithm is the best approach

(5.55)x = 1000

Taking log on both sides

xlog(5.55) = log1000 = 3

log(5.55)= 3/x

Now,

(0.555)y = 1000

ylog(0.555) = log1000 = 3

⇒ [log (5.55/10)] = 3/y

⇒ log (5.55) – log10 = 3/y

⇒ log (5.55) – 1 = 3/y

⇒3/x – log10 = 3/y

⇒3/x – 3/y = log10 = 1

⇒1/x – 1/y = 1/3

Q3. With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), is

Case Sensitivity: No

Answer Type: Equal [CAT 2019, TITA, Permutations and Combinations, Medium]

Answer: [3920]

Case 1:

Dimension of the rectangle with ends of diagonal being (1,1) and (4,6) = 3*5

[3 ways in horizontal direction and 5 ways in vertical direction]

Thus, the total number of paths from (1,1) to (4,6) = (5+3)! /5!3! =56

Case 2:

Dimension of the rectangle with ends of diagonal being (8,10) and (4,6) = 4*4

[4 ways in horizontal direction and 4 ways in vertical direction]

Thus, the number of paths from (4,6) to (8,10) = (4+4)! /4!4! =70

So, the total number of paths from (1,1) to (8,10) via (4,6) = 56*70 =3920

Q4. Two trains A and B were moving in opposite directions, their speeds being in the ratio 5: 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of the length of train A to that of train B is [CAT 2021, TITA, Level: Moderate]

1. 3:2

2. 5:3

3. 2:3

4. 2:1

Ans: [1]

Let the speed of train A is 5x.

The speed of train B is 3x.

And lengths of train A and train B are L1 and L2 respectively.

Situation 1:

The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other.

It implies that the L2 distance will be covered in 46 seconds with the speed of (5x+ 3x= 8x)

L2 = 46(8x)

Situation 2:

Trains took another 69 seconds for the rear ends of the trains to cross each other.

It implies that the L1 distance is covered in 69 sec.

L1 = 69(8x)

L1/L2 = 69(8x)/[46(8x)] = 3/2

L1: L2 = 3: 2

Part-2: CAT 2025 Preparation Tips: CAT DILR tips (Logical Deductions and Connections Reasoning and Data Interpretation)

CAT 2025 Syllabus Topic: Strategy to prepare Routes and Network questions for CAT

Important Concept/Formula Used in CAT mapping and best routes questions

Concepts Used in CAT mapping and best routes problems are given below:

• These problems are basically a special type of D.I. problems that require a high level of understanding.

• These problems are applications of other topics and most topics are related to Permutation and Combination

CAT exam 2025: DILR practice questions for CAT pdf for references

CAT LRDI Questions: CAT Previous Years Questions On Routes and Network

Mapping and best routes questions including network questions CAT are given below:

Read the following paragraph for roots and network questions for CAT:

A new airline company is planning to start operations in the country. The company has identified ten different cities that 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 must decide on a daily schedule.

The underlying principle that they are working on is the following:

Any person staying in any of these 10 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.

Q1) CAT 2025 routes and network questions and answers are given below

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:

1. 45

2. 90

3. 180

4. 135

CAT routes and network problems with solutions are given below

Solution: [C]

The question is simply asking to connect 2 dots out of 10 dots or two stations out of 10 stations this could be done by selecting 2 points out of 10 points that could be done by 10C2 which is 45 but 45 will not be the answer because consider the person is travelling from city A to city B and at the same time an another person must be travelling from city B to city A so we need to multiply 45 by 2 so final answer must be 45*2=90 but this is for morning only so we need to multiply this 90 by 2 for evening also so the final answer must be 90*2=180

Answer (C)

Q2) CAT exam 2025 routes and network Questions with solutions are given below:

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/or 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:

1. 54

2. 120

3. 96

4. 60

Routes and network problems with answers for the CAT exam are given below

Solution: [C]

Consider hubs first there will be 4 flights between two hubs (2 at morning and 2 at evening).

So, there will be 3 hub cities and each route will have 4 flights so we will have a total of 12 cities between 3 hubs

Now consider a direct flight from 3 hub cities to 7 non-hub cities is=

3C1 * 7C1*4 = 84

So, the total number of flights will be = 84 + 12=96

ANSWER (C)

Tricks and Tips for CAT questions on routes and networks

Find the tips and tricks for network questions CAT below:

• These are special types of problems, so these must be needed to be practised before the exam.

• A sound understanding of topics such as Permutation-Combination and number system is been required to solve these questions with agility

CAT entrance exam: Prerequisite to Routes and network

Prerequisites to Routes and Network reasoning are given below

• Puzzles

• Permutation & Combination

References to Study (Theory) Routes and Network for CAT

Best sources to study Routes and Network concepts for CAT exam are given below:

• LRDI by Nishit K. Sinha

• HandaKaFunda

References to Practise Routes and Network problems for CAT

Best sources to practise Routes and Network questions for CAT are given below:

• MBA Entrance Previous years Papers and Sample Papers.

• Elite Grid’s youtube Channel https://www.youtube.com/watch?v=iuVGk7vTuFM&t=69s

• Cat Preparation-iquanta https://www.youtube.com/watch?v=zYTQl1ICzjk

Part-2: CAT 2025 Preparation Tips: CAT DILR tips (Logical Deductions and Connections Reasoning and Data Interpretation)

CAT 2025 Syllabus Topic: Strategy to prepare Routes and Network questions for CAT

Important Concept/Formula Used in CAT mapping and best routes questions

Concepts Used in CAT mapping and best routes problems are given below:

1. These problems are basically a special type of D.I. problems which require a high level of understanding.

2. These problems are applications of other topics and most topics are related to Permutation and Combination.

CAT exam 2025: DILR practice questions for CAT PDF

CAT LRDI Questions: CAT Previous Years Questions On Routes and Network

Mapping and best routes questions including network questions CAT are given below:

Read the following paragraph for roots and network questions for CAT:

A new airline company is planning to start operations in the country. The company has identified ten different cities that 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 must decide on a daily schedule.

The underlying principle that they are working on is the following:

Any person staying in any of these 10 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.

Q1) CAT 2025 routes and network questions and answers are given below

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:

1. 45

2. 90

3. 180

4. 135

CAT routes and network problems with solutions are given below

Solution: [C]

The question is simply asking to connect 2 dots out of 10 dots or two stations out of 10 stations this could be done by selecting 2 points out of 10 points that could be done by 10C2 which is 45 but 45 will not be the answer because consider the person is travelling from city A to city B and at the same time an another person must be travelling from city B to city A so we need to multiply 45 by 2 so final answer must be 45*2=90 but this is for morning only so we need to multiply this 90 by 2 for evening also so the final answer must be 90*2=180

Answer (C)

Q2) CAT exam 2025 routes and network Questions with solutions are given below:

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/or 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:

1. 54

2. 120

3. 96

4. 60

Routes and network problems with answers for the CAT exam are given below

Solution: [C]

Consider hubs first there will be 4 flights between two hubs (2 at morning and 2 at evening).

So, there will be 3 hub cities and each route will have 4 flights so we will have a total of 12 cities between 3 hubs

Now consider a direct flight from 3 hub cities to 7 non-hub cities is=

3C1 * 7C1*4 = 84

So, the total number of flights will be = 84 + 12=96

ANSWER (C)

Tricks and Tips for CAT questions on routes and networks

Find the tips and tricks for network questions CAT below:

• These are special types of problems, so these must be needed to be practised before the exam.

• A sound understanding of topics such as Permutation-Combination and number system is been required to solve these questions with agility

CAT entrance exam: Prerequisite to Routes and Network

Prerequisites to Routes and Network reasoning are given below

• Puzzles

• Permutation & Combination

References to Study (Theory) Routes and Network for CAT

Best sources to study Routes and Network concepts for CAT exam are given below:

• LRDI by Nishit K. Sinha

• HandaKaFunda

References to Practice Routes and Network problems for CAT

Best sources to practise Routes and Network questions for CAT are given below:

• MBA Entrance Previous years Papers and Sample Papers.

• Elite Grid’s youtube Channel https://www.youtube.com/watch?v=iuVGk7vTuFM&t=69s

• Cat Preparation-iquanta https://www.youtube.com/watch?v=zYTQl1ICzjk

Part-3: CAT Exam Preparation 2025: CAT Exam Tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Para Summary” for CAT-2025

Important Concept of CAT para summary questions

• The concepts used in the CAT parasummary questions are given below:

• These questions ask you to summarise a passage (100- 150 words) in a single statement.

CAT Practice Questions on Para Summary from CAT Exam

Para Summary sample question:

Directions for Summary: A paragraph is followed by four options which have summarised the passage in their own way. Pick the option that best summarises the passage:

Developing countries are becoming hotbeds of business innovation in much the same way as Japan did from the 1950s onwards. They are reinventing systems of production and distribution and experimenting with entirely new business models. Why are countries that were until recently associated with cheap hands now becoming leaders in innovation?

Driven by a mixture of ambition and fear, they are relentlessly climbing up the value chain. Emerging-market champions have not only proved highly competitive in their own backyards, they are also going global themselves. [CAT 2021]

Options:

1. Developing countries are being forced to invent new business models which challenge the old business models, so they can remain competitive domestically.

2. Production and distribution models are going through rapid innovations worldwide as developed countries are being challenged by their earlier suppliers from the developing world.

3. Competition has driven emerging economies, once suppliers of cheap labour, to become innovators of business models that have enabled them to move up the value chain and go global.

4. Innovations in production and distribution are helping emerging economies compete with countries to which they once supplied cheap labour.

Solution and Strategy for Para summary for CAT are given below:

Answer: [3]

CAT Tips: Try to pick ‘Subject Matter’

The idea of the paragraph is driven by:

1. Developing economies are becoming hotbeds of economic innovation.

2. A mixture of ambition and fear they are relentlessly climbing up the value chain.

the 3rd option best describes these two ideas.

Directions for Summary: A paragraph is followed by four options which have summarised the passage in their own way. Pick the option that best summarises the passage:

Foreign peacekeepers often exist in a bubble in the poor countries in which they are deployed; they live in posh compounds, drive fancy vehicles, and distance themselves from locals. This may be partially justified as they are outsiders, living in constant fear, and performing a job that is emotionally draining. But they are often despised by the locals, and many would like them to leave. A better solution would be bottom-up peacebuilding, which would involve spending more time working with communities, understanding their grievances and earning their trust, rather than only meeting government officials. [CAT 2021]

1. The environment in poor countries has tended to make foreign peacekeeping forces live in enclaves, but it is time to change this scenario.

2. Extravagant lifestyles and an aloof attitude among the foreigners working as peacekeepers in poor countries have justifiably made them the target of local anger.

3. Peacekeeping forces in foreign countries have tended to be aloof for valid reasons but would be more effective if they worked more closely with local communities.

4. Peacekeeping duties would be more effectively performed by local residents given their better understanding, knowledge and rapport with their own communities.

Answer: [3]

The main idea of the passage can be described by the following points:

Peacekeepers tend to live in a bubble for some reasons.

They will work more effectively if they involve the locals.

Option 3 best describes these ideas.

Tips and Tricks for Para Summary

• Read and understand the paragraph. If you don’t understand the paragraph, you cannot summarise it.

• Pick the subject matter and look for important nouns and try to relate these logically.

• Eliminate the options which are out of context.

• See the SCOPE.

• Skip the question if you are not able to understand.

CAT 2025: Prerequisite to Para Summary

• Reading Comprehension

• Analytical ability

References to Study (Theory) para summary for CAT exam

• How to Prepare for Verbal Ability and Reading Comprehension for CAT | 9th Edition Book by Arun Sharma and Meenakshi Upadhyay

• (YouTube: https://www.youtube.com/watch?v=sidnBLgA7k0)

References to Practise CAT Questions on para summary for verbal sections

• BodheePrep (https://www.youtube.com/watch?v=HZCKA_Zt8-Q&list=PLhsX_kQ8ISVY62xPfBCaSY5r5oNLloHvU)

• (https://www.youtube.com/watch?v=s9zWnyJjA0Y&list=PLhsX_kQ8ISVY62xPfBCaSY5r5oNLloHvU&index=2)

• (https://www.youtube.com/watch?v=aa7n-i98slw&list=PLhsX_kQ8ISVY62xPfBCaSY5r5oNLloHvU&index=3)

Strategies to Ace Route Questions in CAT 2025

Route questions often look confusing at first, but with the right method, they’re actually quite manageable. These questions check how well you understand directions and movement, so it’s important to stay focused and use a step-by-step approach.

• Many beginners focus too much on studying without practising enough questions. Practice is essential to understand concepts and improve speed in CAT 2025.

• Skipping basics creates gaps that make advanced topics harder. A strong foundation helps solve complex problems more easily and confidently.

• Poor time management in CAT 2025 leads to incomplete revision and less practice. Planning your study schedule helps cover the syllabus effectively and reduces stress.

• Relying only on coaching without self-study limits your progress. Consistent self-practice and analysing your mistakes are key to success. You can use these to ace CAT 2025 without coaching.

• Ignoring CAT 2025 mock tests means missing out on real exam practice. Mock tests help build exam temperament and identify areas that need improvement.

CAT 2025 Ebooks by Careers360

CAT 2025 eBooks by Careers360 offer a complete set of study materials, covering all key sections, Quant, VARC, and DILR. These eBooks include tips, practice questions, and strategies tailored to the latest CAT pattern for smarter preparation.

Do your best to prepare and stay focused because Day 58 will be back tomorrow with sample papers based on the CAT 2025 pattern and markings.

Thank you!

All the Best!