CAT 2025 Success Formula: Surfing through Escalators, Venn Diagrams Puzzle Questions, and Participles - Day 34

CAT Preparation 2024 in 60 days

Preparing for CAT 2024 in 60 days requires a focused and strategic approach. With disciplined study, regular practice, and smart revision, you can strengthen key concepts, improve speed, and boost accuracy.

Part-1: Quantitative Aptitude for CAT exam

Important Concept/Formula Used in Time, Speed and Distance escalator problems

Time speed distance escalator problems:

1. Moving ‘with’ the escalator means one has to climb fewer steps on one’s own. (Similar to downstream)

2. Moving ‘against’ the escalator means one has to climb more steps on one’s own. (Similar to upstream)

3. Types of Escalator based problems:

• Length-related questions

• Time-related questions

• Steps-related questions

• Speed-related questions

CAT Exam:

Previous Year CAT Questions On Time, Speed and Distance (Escalator):

Q1. Rakesh takes 45 seconds on an escalator which is moving down when he walks down but takes 35 seconds when he runs down. He takes 25 steps when he walks whereas he takes 35 steps when he is running. What is the total number of steps in the escalator? [TITA, Based on CAT]

Common escalator problems and solutions:

Let the speed of the escalator be ‘x’ steps per second.

tsd CAT Questions Escalator Trick: The distance covered in going down in both cases should be the same.

Distance covered when he is walking = 25 + 45x (45x is covered by escalator)

Distance covered when he is running = 35 + 35x (35x is covered by escalator)

=> 25 + 45x = 35 + 35x

=> x = 1

Total number of steps = 25 + 45(1) = 70 steps

Time speed distance escalator problems

Q2. Amit and Sumit are climbing on a moving escalator that is going up. Amit takes 40 steps to reach the top whereas Sumit takes 45 steps for the same. Sumit takes 5 steps whereas Amit can take only 4 steps in one second. What is the total number of steps in the escalator? [TITA, Based on CAT]

Common escalator problems and solutions:

tsd CAT Questions Escalator Trick 1: First find the time taken by both to reach the top

For Amit, t = 45/5 = 9 seconds

For Sumit, t = 40/4 = 10 seconds

Let the escalator move with a speed of x steps per second.

tsd CAT Questions Escalator Trick 2: The distance covered in going down in both cases should be the same.

=> 9(5 + x) = 10(4 + x)

=> x = 5 steps per second

Number of steps in the escalator = 9(5 + 4) = 81 steps

Prerequisite for Escalator Questions For CAT

• Relative speed

• Upstream and downstream

• Basics of Time, speed and distance

CAT Exam Important Topic: Strategy to Prepare “Escalators (Time, speed and Distance) and Escalator Questions For CAT

Time, Speed and Questions for CAT (Escalator)

• The height of each step does not matter.

• Distance is measured in terms of steps.

• The total steps by a person and the escalator are equal to the number of visible steps.

CAT study material: References to Study (Theory) Escalator Concepts

• Escalator Questions For CAT

• How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition; Pg No 335 to 339)

• Rodha (YouTube, Link: https://www.youtube.com/watch?v=yzLtv86sWgI)

References to Study (Practice)Escalator Questions For CAT

• Quantitative Aptitude for the CAT – Sarvesh Verma.

• Rodha (YouTube, (Link: https://www.youtube.com/watch?v=RHflaojKVlI)

Part-2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2024 Syllabus Topic: Strategy to prepare “Venn Diagram” (Part-2) and Venn Diagram Questions

CAT Exam:

CAT Previous Year Questions on Venn Diagram :

Q1. A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, and 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is?

1. 32

2. 38

3. 43

4. 45

Venn Diagram Questions with Solution: ANS. (3)

According to the information given in the question

Considering that all those who play all their games as X as shown in the above Venn diagram, we will consider Student’s playing football and cricket both as 63-x, Student’s playing football and tennis both will be 58-x and student’s playing cricket and tennis both as 25-x.

Venn Diagram Trick: Firstly, as we know each student is playing at least one game so the addition of all players playing must be equal to the total number of students.

Secondly, as we know student playing game is clearly given in question

So, solution would be like

Only football would be 144-(63-x + x + 58-x) =23+x

Similarly, only tennis would be 123-(58-x+x+25-x) =40+X

Venn Diagram Trick: Students playing all the games must be equal to 256

256= Cricket + only football + only tennis + both football and tennis

256 = 132 + 23+x + 40+x + 58-x

On solving we get

X = 3

So, they have asked for only tennis so we would put x=3 in 40+x

So, answer would be = 40+3=43

Q2. Out Of 60 students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, 16 do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. What are the maximum and the minimum number of people who could have done Chemistry only?

Venn Diagram Questions with Solution:

Trick for Venn Diagram: According to given information, draw Venn diagram as shown below:

All students studying at-least one subject so

P + M+ C +(P&C) = 60

P+M+C+14 = 60

P+M+C = 44

Trick for Venn Diagram: Apply the given condition in equations formed

The number of people who do exactly one of the three is more than the number who do more than one of the three => Only P + only C must be greater than P&M + 16

So,

Only P + Only C > P&M + 16

The Question needs the answer for maximum and minimum for only C

Since they are asking for maximum and minimum of Only C

The trick is for minimum Put only C as 0 and if this equation holds then minimum would be zero

For maximum put only C as 44 and then check for equation hold or not

So, by putting only C as zero we get

Only P+0 > P&M + 16

Now we can easily see that equation will hold, we can find many values for only P and P&M

Similarly, if we put only C as 44 which is maximum value still the equation will hold so the answer would be

Max = 44 and Min = 0

CAT entrance exam: Prerequisite to Venn Diagram Questions

• Set Theory

• Venn Diagram Basics

CAT syllabus 2024: References to Study (Theory) Venn Diagram Concepts

• How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 744- 748)

• https://www.youtube.com/channel/UCHXQiDwicRon0tRuWj6r9HA (Rodha Youtube Channel)

• CAT Exam:

References to Study (Practice) Venn Diagram Questions

• How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 749- 764)

• CAT Previous years Papers and Sample Papers.

Part-3: CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Participles” for CAT-2024

CAT Important Basic Concept

Participles are forms of verbs that can be used as nouns, modifiers, and compound verbs.

CAT Previous Years' Questions on Participles

Find the error in the underlined part:

Question: Due to the slow-moving nature of tectonic plate movement, the oldest ocean crust is thought to date from the Jurassic period, formed from huge fragments of the Earth’s lithosphere and lasted 200 million years. [CAT PYQ]

1. formed from huge fragments of the Earth’s lithosphere and lasted 200 million years.

2. forming from huge fragments of the Earth’s lithosphere and lasting 200 million years.

3. forming from huge fragments of the Earth’s lithosphere and lasted 200 million years.

4. formed from huge fragments of the Earth’s lithosphere and lasting 200 million years.

Solution: [D]

The “oldest ocean crust” was “formed” in the past during the Jurassic period and is currently still around (since the word ‘oldest’ directed towards its presence, otherwise the word ‘oldest’ would not have been used). We need the past tense/participle verbs to be used correctly.

Option (A): The ocean crust was “formed” in the past” but if “lasted” is past tense then the oldest ocean crust is no longer around.

If you chose (B) or (C), “forming” implies the ‘oldest ocean crust is still being formed. and that part is no longer continuing to form but was formed at some point during the Jurassic period.

Option D is correct.

CAT 2024:

Prerequisite

• Verb

• Tenses and Sentence Verb agreement

Tips and Tricks for CAT Exam

• To figure out which role a participle is playing, find the core of the sentence.

• Try to spot the participle in this sentence.

• Present participles always end in “-ing”

• Past participles are generally identical to the past tense form of the verb.

CAT exam: References to Study (Theory)

• Wren and Martin

• Bodhee Prep CAT Preparation (https://www.youtube.com/watch?v=diPZrBHQ7rM)

CAT exam: References to Study (Practice)

• Mastering the Verbal Ability for CAT by Ajay

• CAT Previous years Papers and Sample Papers.

• https://www.youtube.com/watch?v=Ql5ipQILsKM

Free PDFs for CAT 2024 preparation

• CAT preparation strategy by experts

• CAT 2024 Topper Interviews

Tips and Tricks to Solve Venn Diagrams

Venn Diagram questions in the CAT exam appear frequently in the DILR section, testing your ability to understand and organise data involving overlapping sets. With the right techniques and regular practice, you can solve these questions accurately and within time limits.

1. Understand Set Terminology

Tip: Know what union (A ∪ B), intersection (A ∩ B), complement (A′), and subsets mean.

Example: If 40 students like Math (M) and 30 like English (E), A ∪ B = those who like at least one = M + E – M∩E.

2. Start with the Innermost Set

Tip: Begin solving from the part common to all sets (triple intersection in 3-set problems), then move outward.

Example: If 10 students like all three sports—Cricket, Football, and Hockey—place 10 in the intersection of all three circles first before filling other sections.

3. Use Variables for Unknowns

Tip: Assign variables to unknown segments and use given totals to form equations.

Example: If 100 people were surveyed, x like only A, y like A and B, z like all three, create equations:

Total = x + y + z + other regions = 100.

4. Draw Neat, Labelled Diagrams

Tip: Keep the diagram clean with labels for each region (Only A, A∩B, A∩B∩C, etc.).

Example: For a 3-set Venn diagram, label 7 distinct regions. It avoids confusion when plugging in values or solving equations.

5. Practice Common Set Patterns

Tip: Know standard expressions like “Only A” = A – (A∩B + A∩C – A∩B∩C).

Example: If 50 like A, 30 like both A and B, and 10 like all three, then "only A" = 50 – (30 – 10) (A∩C – A∩B∩C).

6. Use Total = A + B + C – (Pairwise Intersections) + (All Three)

Tip: Apply the inclusion-exclusion principle.

Example: If:

• A = 60

• B = 70

• C = 50

A∩B = 30

B∩C = 20

A∩C = 25

A∩B∩C = 15

Then Total = 60 + 70 + 50 – (30 + 20 + 25) + 15 = 120

7. Use Complementary Information Wisely

Tip: Subtract people outside the sets from the total to focus only on those involved.

Example: Out of 200 students, 40 like none of the three subjects. So, only 160 belong inside the Venn Diagram.

Practice and remain focused; Day 35 will be posted tomorrow.