CAT 2026 Success Formula: Surfing through Escalators, Venn Diagrams Puzzle Questions, and Participles - Day 34

1. CAT Quantitative Aptitude: Escalator Problems

Escalator questions are based on the concepts of Time, Speed and Distance (TSD). They generally involve calculating the speed of a moving escalator, the number of steps it contains or the time required to reach the top or bottom.

Important formulas for escalator questions

Revise Time, Speed and Distance and Relative Speed and Average Speed to improve your understanding of rate-based questions.

CAT practice question 1: Find the total number of escalator steps

Rakesh takes 45 seconds to walk down a descending escalator, taking 25 steps himself. When he runs down, he takes 35 steps and reaches the bottom in 35 seconds. Find the total number of steps on the escalator.

Solution:

Let the escalator move at $x$ steps per second.

Since the total number of steps remains constant,

$25+45x=35+35x$

$45x-35x=35-25$

$10x=10$

$x=1$

The total number of steps on the escalator is

$25+45(1)=70$

Answer: 70 steps

CAT practice question 2: Calculate the escalator length

Amit takes 40 steps to reach the top of an ascending escalator, while Sumit takes 45 steps. Amit climbs at 4 steps per second, and Sumit climbs at 5 steps per second. Find the total number of steps on the escalator.

Solution:

Amit's travel time is:

$t_A=\frac404=10$ seconds

Sumit's travel time is:

$t_S=\frac455=9$ seconds

Let the escalator speed be $x$ steps per second. Since both travel the same escalator length:

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

$40+10x=45+9x$

$x=5$

The total number of steps on the escalator is:

$10(4+5)=90$

Answer: 90 steps

Tips to solve escalator questions in CAT

• Set up the distance equation: The escalator length remains constant when the starting and ending points are the same.

• Check the direction of movement: Add speeds when the person and escalator move in the same direction; subtract them when they move in opposite directions.

• Keep units consistent: Convert the information into steps per second or another common unit before calculating.

• Practise related concepts: Revise Time and Work to strengthen your understanding of rate-based problems.

2. CAT DILR: Venn Diagram Questions, Formulas and Shortcuts

Venn diagrams help organise information about overlapping groups, such as students studying different subjects or people participating in multiple sports. CAT DILR questions may ask candidates to calculate the number of people belonging to exactly one group, exactly two groups or all three groups.

Important Venn diagram formulas

For two sets $A$ and $B$:

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

For three sets $A$, $B$ and $C$:

$n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)$

Candidates can revise the Venn Diagram reasoning topic to practise set relationships and common question types.

CAT practice question 1: Find the number of members who play only tennis

A club has 256 members. Of these, 144 play football, 123 play tennis, and 132 play cricket. Additionally, 58 play both football and tennis, 25 play both tennis and cricket, and 63 play both football and cricket. Every member plays at least one game. How many members play only tennis?

Options:

1. 32

2. 38

3. 43

4. 45

Solution:

Let $x$ represent the number of members who play all three games.

Using the inclusion-exclusion principle,

$256=144+123+132-58-25-63+x$

$256=253+x$

$x=3$

The number of members who play only tennis is:

$123-(58-3)-(25-3)-3$

$=123-55-22-3$

$=43$

Answer: Option 3 (43)

CAT practice question 2: Find the minimum and maximum number of students studying only Chemistry

Out of 60 students, everyone studies at least one of Mathematics, Physics, and Chemistry. Every Mathematics student also studies Physics, and no student studies both Mathematics and Chemistry. Sixteen students study both Physics and Chemistry.

The number of students studying exactly one subject is greater than the number studying more than one subject. Find the minimum and maximum possible numbers of students studying only Chemistry.

Solution:

Let:

• $p$ = number of students studying only Physics

• $m$ = number of students studying Mathematics and Physics

• $c$ = number of students studying only Chemistry

The possible groups are only Physics, only Chemistry, Mathematics and Physics, and Physics and Chemistry.

Since 16 students study both Physics and Chemistry,

$p+m+c+16=60$

$p+m+c=44$

The number studying exactly one subject is $p+c$, while the number studying more than one subject is $m+16$.

According to the question,

$p+c>m+16$

Since $p+c=44-m$,

$44-m>m+16$

$28>2m$

$m29$, the condition is satisfied.

Therefore, the minimum number of students studying only Chemistry is $0$.

Maximum number of students studying only Chemistry

To maximise $c$, set $p=0$ and $m=0$.

$c=44-0-0=44$

In this case, 44 students study only Chemistry, and the remaining 16 study Physics and Chemistry. Thus, 44 students study exactly one subject, while 16 study more than one subject.

Since $44>16$, the condition is satisfied.

Answer: Minimum = 0; Maximum = 44 students.

Tips to improve accuracy in Venn diagram questions

• Label each region before starting calculations.

• Check whether pairwise intersections include the triple intersection.

• Verify that the sum of all regions equals the total population.

• Translate conditions such as “at least one” and “exactly one” into equations.

• Practise Logical Deductions and Connections to improve your ability to interpret conditions and identify relationships.

3. CAT VARC: Participles, Grammar Rules and Practice Questions

Participles are verb forms used in verb phrases and modifiers. Understanding present and past participles can help candidates interpret sentence structures and identify grammatical errors. This will help you strengthen your CAT VARC preparation strategy for 2026.

Present participles vs past participles

The correct form depends on the sentence structure and intended meaning. A word ending in -ing is not automatically incorrect, and a past participle does not always indicate a completed action in isolation.

CAT practice question: Identify the correct sentence construction

Question: Choose the option that best replaces the underlined part of the sentence to make it grammatically correct.

The oldest oceanic crust is believed to date back to the Jurassic period, having formed through tectonic processes and surviving for millions of years.

Options:

1. having formed through tectonic processes and surviving for millions of years

2. formed through tectonic processes and survived for millions of years

3. forming through tectonic processes and survived for millions of years

4. having formed through tectonic processes and survived for millions of years

Correct Answer: Option 2

Explanation: The subject, the oldest oceanic crust, is described by two coordinated verb forms: formed and survived. Option 2 maintains parallel grammatical construction and clearly conveys the intended meaning. The other options introduce inconsistent verb forms or awkward constructions.

Tips to revise grammar for CAT

• Identify the main subject and verb before evaluating a sentence.

• Check whether modifiers describe the correct noun or clause.

• Revise subject-verb agreement, verb forms and parallel construction.

• Practise previous-year VARC questions and understand why each incorrect option fails.

CAT 2026 Preparation Resources: Previous-Year Questions and Sample Papers

Use these eBooks and sample papers to practise Quantitative Aptitude, DILR and VARC. Select resources according to the topics you need to strengthen.

Escalator problems, Venn diagrams and participles require different techniques, but all three reward careful reasoning and attention to detail. Revise the relevant concepts, solve practice questions independently and analyse your mistakes to build a more consistent approach to CAT 2026 preparation.

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