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

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.

2. 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

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 :

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:

1. Some people misuse the alarm chain

2. 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:

1. An individual aspires to be a professional

2. 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.