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CAT Success Strategy: Mastering Stats, Clock Questions, and Verbal Ability on Critical Reasoning - Day 53
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CAT 2025 Success Strategy Day 53: On Day 53 of CAT 2025 preparation, focusing on mastering statistics, clock problems, and verbal ability with an emphasis on critical reasoning can provide a significant advantage to aspirants aiming for a top percentile. Targeted practice in data interpretation, time and work-based reasoning, and logical verbal reasoning not only improves speed and accuracy but also enhances overall problem-solving efficiency. By developing a strong grip on these high-weightage CAT topics, candidates can tackle complex questions confidently and optimize their scores. This article shares expert CAT 2025 success strategies, tips, and shortcuts to help aspirants strengthen these crucial areas and maintain consistent preparation momentum.
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.
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,
$\text{Mode} = l + \frac{h(f_1 - f_0)}{(f_1 - f_0) - (f_2 - f_1)}$
Where,
$l$ = Lower limit of modal class
$h$ = Magnitude of the modal class
$f_1$ = Frequency of the modal class
$f_0$ = Frequency of the class preceding the modal class
$f_2$ = Frequency of the class succeeding the modal class
Measures of Dispersion:
The various measures of dispersion are as follows:
Range: $X_{\text{max}} - X_{\text{min}}$, where $X_{\text{max}}$ = Maximum observation, $X_{\text{min}}$ = Minimum observation
Mean Deviation: Average deviation of each observation from the mean value
If $X_1,X_2,......X_N$ is the set of N observations, then its standard deviation is given by
Standard deviation formula:
$\sigma = \sqrt{\frac{1}{N} \sum (X_i - \overline{X})^2} \quad \text{where} \quad \overline{X} \text{ is the AM}$
Variance formula:
$\text{variance} = \sigma^2 = \frac{1}{N} \sum (X_i - \overline{X})^2$
Quartile deviation
10 – 90 percentile range
Statistics Practice Questions From CAT Previous Years Papers
Q1. 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. 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
Tips to Solve Statistics Questions in CAT
Statistics is often tested in questions related to measures of central tendency, dispersion, and data summarization. Below are key strategies:
1. Master Key Statistical Formulas and Their Application
Understand the logic and derivation behind formulas for mean, median, mode, variance, and standard deviation.
Practice questions involving changes in mean or variance when new data is added or values shift.
CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download Now2. Understand Distribution Patterns and Data Spread
Develop the ability to assess data distribution: symmetric, skewed, or patterned.
Helps solve questions on quartiles, outliers, and relative positioning without lengthy calculations.
3. Apply Smart Techniques for Standard Deviation and Variance
Use assumed mean or shortcut formulas to simplify calculations:
$ \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 $
Avoid calculating each squared deviation manually to save time.
4. Don’t Overlook Weighted Mean and Grouped Data
CAT frequently includes grouped data with different sizes and averages.
Use weighted mean formulas and understand how group sizes impact overall results.
5. Solve Percentile, Quartile, and Decile Problems Visually
Use number lines or visual scales to interpret percentiles, quartiles, and deciles.
Visualizing data simplifies interquartile range calculations and cut-off determinations.
6. Leverage Option Elimination in Approximate Calculations
CAT statistics questions often have numerically close options.
Use approximation, estimation, and bounding techniques to eliminate unlikely answers 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
60 minutes space = 3600
Hour hand covers 3600 in 12 hrs
Minute hand covers 3600 in 60 minutes
Second-hand covers 3600 in 1 minute
The angle between the hour hand and minute hand at h hrs and m minutes
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 :
Clock-based questions in the CAT exam test your ability to calculate angles, relative positions, and time adjustments. Practicing these examples improves speed, accuracy, and problem-solving efficiency.
Question:
The time in a clock is 20 minutes past 2. Find the angle between the hands of the clock. [CAT 2016]
Options:
60 degrees
120 degrees
45 degrees
50 degrees
Solution:
The formula to calculate the angle between the hour and minute hands is:
$ \text{Angle} = \left| \frac{11}{2}M - 30H \right| $
Where $H$ = hour, $M$ = minutes.
Substitute $H = 2$ and $M = 20$:
$ \text{Angle} = \left| \frac{11 \times 20}{2} - 30 \times 2 \right| = |110 - 60| = 50^\circ $
Answer: Option 4 – 50 degrees
Question:
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 the clock show exactly 14 days later? [CAT 2016]
Options:
1:36:48
1:40:48
1:41:24
10:19:12
Solution:
One week has $7 \times 24 = 168$ hours.
During the first week, the clock loses 1%, i.e., $1.68$ hours less.
During the second week, it gains 2%, i.e., $3.36$ hours more than the actual time.
Net gain over two weeks = $3.36 - 1.68 = 1.68$ hours.
Convert 1.68 hours into hours, minutes, and seconds:
$1.68$ hours = 1 hour + 0.68 × 60 minutes = 1 hour 40.8 minutes = 1 hour 40 minutes 48 seconds.
Answer: Option 2 – 1:40:48 P.M.
Tips to Solve Questions on Clock Concepts for CAT 2025
Clock-based questions in the CAT exam are part of the Logical Reasoning section. They test your understanding of angles, positions, and relative motion of clock hands. Mastering these concepts allows you to solve problems accurately and quickly.
Use the Standard Angle Formula
The fundamental formula to calculate the angle between the hour and minute hands is:
$ \theta = \lvert 30H - 5.5M \rvert $
where $H$ is the hour and $M$ is the minutes. This formula is the basis for most CAT clock problems and helps in solving both acute and obtuse angle questions efficiently.
Understand the Relative Speed of Clock Hands
The minute hand moves 6° per minute, while the hour hand moves 0.5° per minute.
Their relative speed of 5.5° per minute is key to solving problems involving overlaps, gaps, or specific angle formations between the hands.
This concept simplifies calculations for questions like when the hands meet or are opposite each other.
Master Overlap and Opposite Positions
The hands overlap every 65 5/11 minutes.
Opposite positions (180° apart) occur 32 8/11 minutes after each overlap.
Memorizing these intervals helps you solve angle-based or meeting-time problems quickly during the exam.
Solve "Mirror Image" Clock Questions Logically
For mirror image questions, subtract the given time from 11:60 to get the reflected time.
Example: The mirror image of 3:40 is 8:20.
This trick prevents confusion and ensures accuracy under time pressure in the CAT exam.
Account for Hour Hand Movement During Minutes
The hour hand moves continuously at 0.5° per minute.
Always account for this motion in angle calculations, especially for questions involving acute angles or exact time-based positions.
Ignoring this movement often leads to wrong answers.
Practice Time Gaps and Specific Time Conditions
CAT often includes problems like finding the time between two events, e.g., when hands are 90° apart.
Create equations using angle = relative speed × time to calculate these gaps accurately.
Consistent practice with these time and angle relationships builds fluency and reduces calculation errors.
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.
Understanding Statements and Assumptions in CAT
A Statements and Assumptions question typically has three parts: Statement, Question, and Options (Assumptions).
Statement:
A statement is a sentence that is expressible and can be either true or false.
Assumptions:
Logically connected to the statement
Relevantly assumed
May or may not be true
These questions test critical reasoning, decision-making, conclusion derivation, and theme detection in the CAT exam.
Q 1. 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]
Options:
Only assumption I is implicit
Only assumption II is implicit
Either I or II is implicit
Neither I nor II is implicit
Both I and II are implicit
Answer: Option E – Both I and II are implicit
Explanation:
The penalty exists because some people misuse the facility, making Assumption I implicit.
The alarm chain is provided for emergency stopping of the train, so Assumption II is also implicit.
Q 2. 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 desires to achieve something that is hard-earned [XAT 2019]
Options:
Only assumption I is implicit
Only assumption II is implicit
Either I or II is implicit
Neither I nor II is implicit
Both I and II are implicit
Answer: Option B – Only assumption II is implicit
Explanation:
Assumption I is not implicit, as the statement does not confirm professional aspiration.
Assumption II is implicit because the statement implies a preference for achievements that are hard-earned, not easy-to-obtain goals.
Tips to Solve Questions on Statements and Assumptions for CAT 2025
Statement and assumption questions in the CAT exam assess your logical reasoning and critical thinking skills. These questions require identifying implicit ideas or beliefs behind a statement, 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 does not explicitly state.
Focus on the unstated but necessary ideas behind the statement to identify correct options.
2. Avoid Extreme Language
Assumptions with absolute terms like “always,” “never,” or “only” are usually incorrect in CAT.
The exam prefers moderate and logically necessary assumptions over extreme or generalized statements.
Look for options that directly support the statement without overstating it.
3. Differentiate Between Assumption and Inference
Assumptions are unstated beliefs that must hold true for the statement to be valid.
Inferences are conclusions derived from the statement.
Avoid confusing the two; focus on what is logically required, not what can be concluded.
4. Test Assumptions Using the Negation Method
Apply the negation test: negate the assumption and check if the statement still holds.
If negating the assumption weakens or invalidates the statement, it is likely a valid assumption.
This method helps eliminate incorrect options systematically and improves speed.
5. Watch for Scope Alignment
Ensure the assumption is directly relevant to the statement.
If the assumption addresses a broader or unrelated issue, it is likely incorrect.
Valid assumptions must align in scope and context with the given statement.
ebooks to Ace CAT 2025 Exam Preparation
Accessing the right ebooks for CAT 2025 preparation can significantly boost your study efficiency. These resources cover Quantitative Aptitude, VARC, DI & LR, and provide practice questions, formulas, and mock tests to help aspirants prepare smartly and ace the exam.
| Title | Download Now |
3000+ Most Important Words - Vocabulary Builder | |
500+ Most Important Idioms and Phrases | |
300+ Most Important Phrasal Verbs | |
CAT 2025 Verbal Ability and Reading Comprehension (VARC) Study Material | |
Permutation & Combination - Video Lectures and Practice Questions | |
Mastering DILR Questions with Expert Solutions | |
CAT 2025 Exam's High Scoring Chapters and Topics | |
Mastering CAT Exam: VARC, DILR, and Quant MCQs & Weightages | |
CAT 2025 Mastery: Chapter-wise MCQs for Success for VARC, DILR, Quant | |
CAT 2025 Quantitative Aptitude Questions with Answers | |
CAT DILR Questions with Solution, Download LRDI Questions for CAT |
Frequently Asked Questions (FAQs)
Q: What are TITA questions in the CAT exam?
A:
TITA (Type In The Answer) questions require you to directly input the numerical answer instead of selecting from options. They test accuracy, conceptual clarity, and calculation speed.
Q: How can I calculate the angle between clock hands quickly?
A:
Use the formula $ \text{Angle} = \left| \frac{11}{2}M - 30H \right| $ where $H$ is the hour and $M$ is minutes. Knowing the relative speed of hour and minute hands helps solve problems efficiently.
Q: How should I practice TITA questions for CAT?
A:
Solve previous year questions and sample papers under timed conditions. Focus on precision, formula application, and reasoning skills rather than guesswork.
Q: How can I improve speed and accuracy in CAT Quantitative Aptitude?
A:
Regularly practice formula-based problems, shortcuts, and previous year questions. Track mistakes, revise key formulas, and solve TITA and clock problems under timed conditions.
Q: How can I improve accuracy in CAT Critical Reasoning questions?
A:
Focus on identifying assumptions, strengthening/weakening arguments, and eliminating answer choices logically. Practice daily with RC-based critical reasoning sets to sharpen analytical skills under timed conditions.
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Have a question related to CAT ?
The three key formulas that can solve almost all Profit & Loss problems are:
-
Profit/Loss % = (Profit or Loss / Cost Price) × 100%, where CP is the cost price.
-
Discount % = (Discount / Marked Price) × 100%, where MP is the marked price.
-
Mark up % = (Mark up Value / Cost Price) × 100%, where CP is the cost price.
These formulas can be adapted for problems involving discounts, marked price, or successive gains/losses.
For detailed examples and variations, you can from the article
With a 70 percent in CAT Examination, you can go for various B-Schools or private collages. The S. K. Patel Institute of Management in Gandhinagar is an option for those who score 70-80 percent in their CAT examination or The Gujarat Institute of Management (GIM) in Goa with a cutoff of 60-80 percentage. These are the collages you can look for in Gujarat or nearby.
Collage in other regions: BA Colleges Accepting 70-80 Percentile in CAT 2025
Thank You.
Hello dear candidate,
NO. your application for CAT will not rejected for wrong gender small mistake in the OBC NCL certificate. You will be considered as an OBC candidate.
Hello,
Here are some top MBA colleges in India with fees under Rs. 2 lakh and their exam/cutoff details:
-
SIMSREE, Mumbai – Fee around Rs. 1.3–1.4 lakh for 2 years. Accepts CAT, CMAT, MAH-CET, MAT, ATMA. Cutoff is very high, usually 99+ percentile in CAT/CMAT.
-
PUMBA (Dept. of Management Sciences, Savitribai Phule Pune University) – Fee around Rs. 1.2–1.3 lakh. Accepts CAT, CMAT, MAH-CET, ATMA. Cutoff approx. 75+ percentile in CAT, 90–95+ percentile in CMAT, high scores in MAH-CET.
-
TISS, Mumbai (MA HRM & other management-related programmes) – Fee around Rs. 1.7–1.9 lakh. Accepts CAT for some courses. Qualifying cutoff is around 60–70 percentile, but final selection cutoffs are higher.
These are the main government institutes where the full MBA/PG programme fee is within Rs. 2 lakh. Cutoffs vary slightly each year and by category, but SIMSREE and PUMBA generally need high scores, while TISS has its own process along with CAT shortlisting.
Hope it helps !
Hey! With a NEET score of 344 in the ST category, it is highly unlikely to get admission in any government BDS college in Delhi through the All India Quota. The cutoff for government BDS seats in Delhi usually falls around 400–450 for ST category, so your score is below that range.
You can consider private dental colleges, state quota seats in other states, or reattempt NEET next year to improve your chances.
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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