CAT Success Strategy: Mastering Stats, Clock Questions, and Verbal Ability on Critical Reasoning - Day 53

CAT 2025 Success Strategy Day 53: Preparing for CAT 2025 can be challenging, but focusing on the right topics makes a big difference. On Day 53 of your preparation, you should master Statistics, Clock questions, and Verbal Ability in Critical Reasoning. Statistics helps you handle data-related problems in Quant, while Clock aptitude questions test your skills in logical reasoning about time and angles. Practising topics mentioned in CAT Syllabus 2025 regularly will boost your accuracy and speed, giving you an edge on exam day. In this article, we have discussed the questions related to Statistics, tips to solve questions and download ebooks for different subjects to get successful MBA admissions 2025-2027.

Check out the CAT 2025 Syllabus

Also read: CAT 2025 QA Syllabus

CAT 2025 DILR Syllabus

CAT 2025 VARC Syllabus

Part-1: Quantitative Aptitude for CAT 2025 exam

Quantitative Aptitude in the CAT 2025 exam evaluates your numerical ability, mathematical concepts, and problem-solving skills. The Quantitative Aptitude syllabus has topics like Arithmetic, Algebra, Geometry, and Number Systems. Hence, this section is critical for achieving a high overall percentile in CAT 2025.

Important Concept/Formula Used in Statistics questions and answers for CAT 2025.

Concepts and Formulas Used in CAT statistics MCQ are given below:

1. Measures of Central Tendency:

The following are the five measures of central tendency.

• Arithmetic mean: AM of a and b is (a+b)/2.

• Geometric mean: GM of a and b is (ab)/2.

• Harmonic mean: Calculated with the help of AP.

• Median (Mid Value): the value of the variable which divides the group into two equal parts.

• Mode: the value of the variable corresponding to the maximum frequency. In the case of continuous frequency distribution, the class corresponding to the maximum frequency is called the modal class and the value of mode is obtained as,

Where,

l = Lower limit of modal class

h = Magnitude of the modal class,

$f_1$= frequency of the modal class

$f_0$= Frequency of class preceding the modal class

$f_2$= Frequency of class succeeding the modal class.

2. Measures of Dispersion:

The various measures of dispersion are as follows

Range ($X_{max}–X_{min}$); $X_{max}–\text{Maximum Observation};X_{min}=\text{Minimum Observation}$

Mean deviation: Average deviation of each observation from the mean value.

3. Standard deviation:

4. Variance

D. Quartile deviation

E. 10 – 90 percentile range

Statistics Practice Questions For CAT Exam From CAT Previous Years Papers

Q1. CAT 2025 Statistics Questions and Answers are given below:

Five positive integers have their mean, mode and median, each equal to 8. If their range is 15 and the mode is unique. How many possible values can the least of them take? [TITA, Based on CAT]

Ans: [1]

Mean = 8

Mode = 8

Median = 8

It means, 8 is the mid-value.

Case 1: Since the mode is unique, 8 occurred a minimum of two times.

Possible case:

a. five values are x y 8 8 x+15 (since the range is 15, where x is the minimum value)

So, (x+ y+ 8+ 8+ x+15) = 8* 5 = 40

⇒ 2x +y = 9

y= 1, x =4 (Not possible; y> x)

y= 3, x = 3 (Not possible; if it is so mode will have two values but mode should be unique)

y= 5, x = 2

One value of x is possible from here.

b. five values be x 8 8 z x+15

So, (x+ 8+ 8+ z+ x+15) = 8* 5 = 40

⇒ 2x +z = 9

z= 1, x =4 (Not possible; x> z)

z= 3, x = 3 (Not possible, z should be greater than 8)

z= 5, x = 2 (Not possible, z should be greater than 8)

Case 2: If 8 occurred three times.

Possible values are x 8 8 8 x+15

So, (x+ 8+ 8+ 8+ x+15) = 8* 5 = 40

⇒ 2x = 1

⇒ x = ½ (not an integer)

From all the cases discussed, there is only 1 possible value of x.

Q2. Statistics test questions are given below:

Rajesh’s family went for a winter vacation by a personal CAR. The prices of oil differ from state to state. Calculate the median oil cost.

81.65, 81.85, 81.90, 91.74, 92.06, 92.10, 102.18 [TITA, Based on CAT]

Solution: Arrange the data in ascending order, we get:

81.65, 81.85, 81.90, 91.74, 92.06, 92.10, 102.18

Hence, the median oil cost is 91.74

CAT Exam Important Topic: Strategy to Prepare “Statistics Questions for CAT”

Find the CAT tips and tricks for Statistics in the Quantitative Section below:

1. The difference between a continuous variable and a discrete variable should be clear.

2. Frequency and cumulative frequency are two different things.

3. Learn all the statistics theorems, including the central limit theorem, LLN, Cauchy representation, mean, median, and mode.

4. Learn series like the Taylor series, Cauchy series, and infinite series as they are used to frame statistical questions.

5. Mode = 3 x median- 2 x mean

6. Practice CAT questions on statistics from Previous years questions to get familiar with the types of questions being asked.

CAT entrance exam: Prerequisite to statistics questions and answers

1. Data Analysis

2. Data Visualisation

CAT study material: References to Study (Theory) Statistics concepts

1. How to Prepare Quantitative Aptitude by Arun Sharma (7th Edition)

2. Rodha: YouTube (https://www.youtube.com/watch?v=VlYCQXSHutM)

3. (https://www.youtube.com/watch?v=zWI2Nv5_7iE)

CAT study material: References to Practise Statistics questions and answers and Statistics interview questions

Study sources of Statistics practice questions for the CAT exam are given below:

1. Objective Arithmetic by Rajesh Verma.

2. CareerRide (https://www.youtube.com/watch?v=6Jrb4wEloCQ )

3. Practice Sample Papers

Tips to Solve Questions on Statistics

Statistics forms an important part of the Quantitative Aptitude section in the CAT exam. Questions from this topic often test your conceptual clarity on measures of central tendency (mean, median, mode), dispersion (range, variance, standard deviation), and data summarisation techniques such as percentiles and quartiles.

1. Master Key Statistical Formulas and Their Application
Go beyond rote learning and focus on understanding the derivation and logic behind formulas for mean, median, mode, standard deviation, and variance. CAT often frames questions that test your depth of understanding. This includes changes in mean when new data is added or effects on standard deviation when values shift.

2. Understand Distribution Patterns and Data Spread
CAT questions have an interpretation of data distribution whether it is symmetric, skewed, or follows a specific pattern. Developing the ability to assess distribution helps in solving questions related to quartiles, outliers, and relative positioning without exhaustive calculations.

3. Apply Smart Techniques for Standard Deviation and Variance
Use deviation methods such as assumed mean or short-cut formulas for variance to simplify long computations. For instance, instead of calculating each squared deviation manually, apply:

$

\mathrm{Var}(X) = \frac{1}{n} \sum_{i=1}^{n} x_i^2 - \left( \frac{1}{n} \sum_{i=1}^{n} x_i \right)^2

$

4. Don’t Overlook Weighted Mean and Grouped Data
CAT exams frequently include questions involving groups with different sizes and averages. To solve these, always use weighted average formulas and understand the impact of group size on overall data.

5. Solve Percentile, Quartile, and Decile Problems Visually
Use number lines or visual scales to understand percentiles, quartiles, and deciles. Visualising the data distribution allows for intuitive understanding, especially when interpreting interquartile ranges or determining cut-off values in a data set.

6. Leverage Option Elimination in Approximate Calculations
Statistics questions in CAT often have numerically close answer options. Train yourself to approximate using logical checks, estimation techniques, or bounding values to rule out unlikely choices, especially under time pressure.

Part 2: CAT 2025 DILR tips (Logical Reasoning and Data Interpretation questions for CAT)

The DILR section of the CAT exam tests your logical reasoning and data interpretation abilities through puzzles, charts, and complex data sets. Mastering questions based on the CAT DILR Syllabus requires strategic thinking, structured analysis, and consistent practice with diverse problem types.

Important Concepts & Formula on Clock Problems

1. 60 minutes space = 3600

2. Hour hand covers 3600 in 12 hrs

3. Minute hand covers 3600 in 60 minutes

4. Second-hand covers 3600 in 1 minute

5. The angle between the hour hand and minute hand at h hrs and m minutes

6. Angle =11/2m-30h

After completing all the important topics and concepts, aspirants should be able to solve Clock questions with solutions for CAT exam 2025 given below.

CAT 2025 Previous Years Questions on Aptitude Clock Concepts

For the practice of all the aspirants, the CAT Logical Reasoning Quiz on: Clock questions and answers are given below :

Q1. Clock aptitude questions for CAT exam are given below:

The time in a clock is 20 minutes past 2. Find the angle between the hands of the clock.

[CAT 2016]

1. 60 degrees

2. 120 degrees

3. 45 degrees

4. 50 degrees?

Solution: [4]

Angle =11/2m-30h

⇒ Angle = 11x 20/2 – 30 x 2= 110 -60 = 500

Q2. CAT Questions Based on the Clock are given below:

A clock loses 1% time during the first week and then gains 2% time during the next week. If the clock was set right at 12 noon on a Sunday, what would be the time that the clock would show exactly 14 days from when it was set right?[CAT 2016]

1. 1: 36: 48

2. 1: 40: 48

3. 1: 41: 24

4. 10: 19: 12

Ans: [2]

One week has 7 * 24 = 168 hours.

If the clock loses 1% time during the first week, then it will show a time of 1% less than 168 hours = 1.68 hours less.

Subsequently, in the second week, it gains 3.36 hours more than the actual time.

As it lost 1.68 hours during the first week and then gained 3.36 hours the next week, the net gain = 1.68 hours.

So the clock will show a time which is 1.68 hours more than 12 Noon two weeks after the given time.

1.68 hours = 1 hour and 40.8 minutes = 1 hour + 40 minutes + 48 seconds.

i.e. 1: 40: 48 P.M

CAT 2025 Syllabus Topic: Strategy to prepare Clock - Concepts and Questions with Solutions for CAT Exam

Clock aptitude questions and formulas are given below:

1. Learn the concepts very carefully.

2. The minute hand and hour hand are perpendicular 22 times in 12 hrs.

3. The minute hand and hour hand are at 1800 for 11 times in 12 hrs.

4. Minute hand and hour hand overlap 11 times in 12 hrs.

5. Learn the concept of a Faulty Clock.

6. Clock which is fast, always gains.

7. Clock which is slow, always loses time.

CAT entrance exam: Pre-requisite to Aptitude Clock Concepts

1. Ratio and Proportion

2. Time, Speed and Distance

3. Knowledge of Analogue Clock

References to Study (Theory) Aptitude Clock Concepts for CAT 2024

1. R S Agrawal

2. (https://www.youtube.com/watch?v=e88HawPKlz8)

References to Practice Clock aptitude questions for the CAT exam

MBA Entrance Previous years Papers and Sample Papers.

Unacademy CAT (https://www.youtube.com/watch?v=_Pj2A5ektTE)

Tips to Solve Questions on Clock Concepts

Clock-based questions in the CAT exam are a part of logical reasoning that test your grasp of angles, positions, and relative motion of clock hands. These problems require precision in applying concepts of circular motion and time calculations.

Use the Standard Angle Formula
Apply the key formula to calculate the angle between the hour and minute hands:

θ=∣30H−5.5M∣
where H is the hour and M is the minutes. This formula forms the basis of most clock problems in CAT.

Understand the Relative Speed of Clock Hands
Recognise that the minute hand moves at 6° per minute while the hour hand moves at 0.5° per minute. Their relative speed (5.5° per minute) is crucial when solving questions about when the hands meet, overlap, or form specific angles.

Master Overlap and Opposite Positions
Hands overlap every 65 5/11 minutes. Opposite hands (180° apart) occur every 65 5/11 ÷ 2 = 32 8/11 minutes after each overlap. Memorising these values helps quickly solve meeting and angle-based questions.

Solve "Mirror Image" Clock Questions Logically
In mirror image problems, subtract the given time from 11:60 to find the reflected time. For example, the mirror image of 3:40 is 8:20. This trick avoids confusion and ensures accuracy under time constraints.

Account for Hour Hand's Movement During Minutes
When solving for angles or positions, don’t treat the hour hand as fixed. It moves as the minute progresses (0.5° per minute), and ignoring this leads to wrong answers—especially in minute-sensitive questions like acute angle formation.

Practice Time Gaps and Specific Time Conditions
CAT may include problems where you must find the time between two events (e.g. when the hands are 90° apart). Build fluency in solving such problems by creating equations based on angle and time relationships, using relative motion consistently.

Part-3: CAT 2025 Verbal Ability & Reading Comprehension

Scoring well in VARC requires daily reading practice, strong vocabulary, and familiarity with a wide range of writing styles. Consistent practice with topic-specific eBooks, sectional tests, and past year papers will help strengthen accuracy for CAT 2025.

Aspirants can download the CAT Critical Reasoning: Decision-making conclusion derivation and theme detection pdf.

Important Concept for CAT Statement and Assumptions (Critical Reasoning: Decision making conclusion derivation and theme detection in CAT)

The question has three parts

Statement + Question+ Options (Assumptions)

Statement: A statement is defined as that which is expressible by a sentence and is either true or false.

Assumptions:

• It is logically connected

• Relevantly assumed

• No surety of being true

CAT Practice Questions on Statements and Assumptions ( Critical Reasoning: Decision making conclusion derivation and theme detection questions for CAT)

Q1. Statements and Assumptions ( Critical Reasoning: Decision making conclusion derivation and theme detection for CAT Exam) are given below:

Statement: A warning in a train compartment – “To stop the train, pull the chain. Penalty for improper use 500”

Assumptions:

Some people misuse the alarm chain

On certain occasions, people may want to stop a running train [NMAT 2020]

1. Only assumption I am implicit

2. Only assumption II is implicit

3. Either I or II is implicit

4. Neither I nor II is implicit

5. Both I and II are implicit

Ans. Option E

Explanation:

If the penalty is imposed then there must be a reason that people are mid using the facility.

So, Assumption 1 is implicit.

Secondly, an Alarm chain is provided for emergency uses. Therefore, II is also implicit.

Q2. CAT exam 2025 statements and Assumptions questions with solutions are given below:

Statement: If it is easy to become an engineer, I don’t want to be an engineer.

Assumptions:

An individual aspires to be a professional

One desire to achieve a thing which is hard-earned [XAT 2019]

1. Only assumption I am implicit

2. Only assumption II is implicit

3. Either I or II is implicit

4. Neither I nor II is implicit

5. Both I and II are implicit

Ans: [B]

Explanation:

If I want to be a professional, I should have worked hard. And I should not deny being an Engineer. Secondly, we can say a statement and assumption are not co-related. so, I is not implicit.

The statement also gives us a hint that one rejects a thing that is easy to achieve. so, Assumption II is implicit.

CAT Exam Important Topic: Strategy to Prepare “Statement and Assumptions” (Critical Reasoning: Decision making conclusion derivation and theme detection ) for CAT-2025

1. Refrain from using basic General Knowledge.

2. Spend adequate time decoding the statement.

3. Increase the level of questions while practising.

4. Any assumption can be accepted if it is:

• the Root Cause of a statement, or

• The desired effect of a statement.

5. Check whether an assumption is implicit or not, by “Keeping yourself in the shoes of the subject”

6. Be careful of the extreme words used in the sentence, such as most, only, all, best, definitely etc. The statement is supposed to be read carefully to pick the right assumption.

7. Practice questions daily (Fewer questions but daily)

CAT 2025: Pre-requisite to Statement and Assumptions

1. Knowledge of basic components of statements and arguments.

2. Sentence Structure.

References to Study (Theory)Statement and Assumptions” (Critical Reasoning : Decision making conclusion derivation and theme detection )

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

2. CAT2CET (YouTube: https://www.youtube.com/watch?v=4hJRh8YIyo0)

References to Study (Practice) questions on Statement and Assumptions

1. Verbal Reasoning by Disha Experts (kindle)

2. CATKing.in

3. (https://www.youtube.com/watch?v=YrBMjb_kb28)

Tips to Solve Questions on Statements and Assumptions

Statement and assumption questions in the CAT exam test your logical reasoning and critical thinking. These questions require you to identify implicit beliefs or ideas behind given statements, making conceptual clarity and analytical precision essential.

1. Identify the Hidden Premise
Read the statement carefully and ask: What must be true for this statement to hold? The assumption is often a hidden condition or belief that the speaker takes for granted but doesn’t explicitly state.

2. Avoid Extreme Language
Assumptions with absolute terms like “always,” “never,” or “only” are usually incorrect. CAT expects nuanced reasoning, so prefers moderate and logically necessary assumptions over extreme or generalised statements.

3. Differentiate Between Assumption and Inference
Don’t confuse assumptions with inferences. Assumptions are unstated beliefs behind the statement, while inferences are conclusions derived from it. Focus on what must be assumed for the statement to be valid.

4. Test Assumptions Using the Negation Method
Use the negation test: if negating the assumption weakens or invalidates the statement, then it is a valid assumption. This is a powerful technique for eliminating incorrect options systematically.

5. Watch for Scope Alignment
Ensure the assumption aligns in scope with the original statement. If the assumption addresses a broader or completely unrelated issue, it is likely incorrect. Assumptions must be directly relevant to the context of the given statement.

Top Ebooks to Ace CAT 2025 Exam Preparation

Top eBooks for CAT 2025 VARC preparation are invaluable for building a strong foundation in Reading Comprehension, Para Jumbles, Grammar, and Vocabulary. The CAT VARC eBooks by Careers360 provide structured, topic-wise content, expert strategies, and a wide range of practice exercises to enhance speed and precision. These are tailored for targeted learning, these resources help you sharpen your verbal reasoning skills. Explore the best eBook links to power your CAT 2025 prep today.