CAT Quantitative Aptitude Previous Year Questions with Solutions

Download CAT Quant Previous Year Questions PDF with Detailed Solutions

CAT Year	Slot 1	Slot 2	Slot 3
2025	Download CAT 2025 QA Slot 1 PDF	Download CAT 2025 QA Slot 2 PDF	Download CAT 2025 QA Slot 3 PDF
2024	Download CAT 2024 QA Slot 1 PDF	Download CAT 2024 QA Slot 2 PDF	Download CAT 2024 QA Slot 3 PDF
2023	Download CAT 2023 QA Slot 1 PDF	Download CAT 2023 QA Slot 2 PDF	Download CAT 2023 QA Slot 3 PDF
2022	Download CAT 2022 QA Slot 1 PDF	Download CAT 2022 QA Slot 2 PDF	Download CAT 2022 QA Slot 3 PDF
2021	Download CAT 2021 QA Slot 1 PDF	Download CAT 2021 QA Slot 2 PDF	Download CAT 2021 QA Slot 3 PDF
2020	Download CAT 2020 QA Slot 1 PDF	Download CAT 2020 QA Slot 2 PDF	Download CAT 2020 QA Slot 3 PDF

CAT Quant Exam Pattern

The following table presents the recent CAT 2025 Quantitative Aptitude (QA) examination structure.

Exam Parameter	CAT Quant Pattern
Section Name	Quantitative Aptitude (QA)
Questions	22
Maximum Marks	66
Sectional Time Limit	40 minutes
Marks for Each Correct Answer	3 marks
Negative Marking for Incorrect MCQs	-1 mark
Negative Marking for TITA Questions	No negative marking
Question Formats	Multiple Choice Questions (MCQs) and Type in the Answer (TITA)

CAT Quant Topic-Wise Priority

Topic Area	Important Subtopics	Preparation Priority
Arithmetic	Percentages, profit and loss, ratios, averages, mixtures, time and work, speed-distance-time, simple and compound interest	High
Algebra	Linear and quadratic equations, inequalities, functions, logarithms, progressions	High
Geometry and Mensuration	Triangles, circles, polygons, coordinate geometry, areas and volumes	Medium to High
Number Systems	Divisibility, remainders, factors, LCM, HCF, surds and indices	Medium
Modern Mathematics	Permutations and combinations, probability, set theory, sequences and series	Medium

CAT Arithmetic Questions with Solutions

Arithmetic covers percentages, profit and loss, ratios, averages, mixtures, time and work, speed-distance-time and interest. Most questions require aspirants to convert the given information into mathematical relationships before applying the relevant formula.

Question 1: Percentages and Profit and Loss

Question: A trader marks an article 60% above its cost price. He then offers a discount of 25% on the marked price. What is his profit percentage?

Solution:

Assume the cost price (CP) is ₹100.

Step 1: Calculate the marked price.

Marked Price = Cost Price + 60% of Cost Price

= 100 + (60/100 * 100)

= ₹160

Step 2: Calculate the discount.

Discount = 25% of ₹160

= (25/100) * 160

= ₹40

Step 3: Calculate the selling price.

Selling Price = Marked Price - Discount

= 160 - 40

= ₹120

Step 4: Calculate the profit percentage.

Profit = Selling Price - Cost Price

= 120 - 100

= ₹20

Profit Percentage = (Profit / Cost Price) * 100

= (20/100) * 100

= 20%

Final Answer: 20% profit.

Shortcut Method: Successive Percentage Change

A 60% increase gives a multiplier of 1.60, while a 25% decrease gives a multiplier of 0.75.

1.60 * 0.75 = 1.20

The selling price is 1.20 times the cost price. Therefore, the trader earns a 20% profit.

Question 2: Time, Speed and Distance

Question: A train covers 360 km in 4 hours. If it increases its speed by 15 km/h, how long will it take to cover the same distance?

Solution:

Step 1: Calculate the original speed.

Speed = Distance / Time

= 360 / 4

= 90 km/h

Step 2: Calculate the new speed.

New Speed = 90 + 15

= 105 km/h

Step 3: Calculate the new travel time.

Time = Distance / Speed

= 360 / 105

= 24/7 hours

= 3 3/7 hours

Convert the fractional part into minutes:

(3/7) * 60 = 180/7

= 25 5/7 minutes

Final Answer: 3 hours 25 5/7 minutes, or approximately 3 hours 26 minutes.

Shortcut Method: Inverse Proportionality

When distance remains constant, speed and time are inversely proportional.

T2 = T1 * (S1/S2)

= 4 * (90/105)

= 24/7 hours

The train requires 3 hours 25 5/7 minutes to cover the distance.

Question 3: Time and Work

Question: A can complete a task in 12 days, while B can complete the same task in 18 days. They work together for 4 days. What fraction of the work remains?

Solution:

Step 1: Calculate individual work rates.

A's one-day work = 1/12

B's one-day work = 1/18

Step 2: Calculate their combined work rate.

Combined one-day work:

1/12 + 1/18

= (3 + 2)/36

= 5/36

Step 3: Calculate the work completed in 4 days.

Work completed:

4 * (5/36)

= 20/36

= 5/9

Step 4: Calculate the remaining work.

Remaining Work = 1 - 5/9

= 4/9

Final Answer: 4/9 of the work remains.

Shortcut Method: LCM Approach

Take the total work as 36 units, the LCM of 12 and 18.

• A completes 3 units daily.
• B completes 2 units daily.
• Together, they complete 5 units daily.

Work completed in 4 days = 5 * 4 = 20 units.

Remaining work = 36 - 20 = 16 units.

Remaining fraction = 16/36 = 4/9.

CAT Algebra Questions with Solutions

Algebra tests equations, inequalities, functions, logarithms, progressions and algebraic manipulation. The questions often require aspirants to translate given conditions into equations and apply mathematical properties.

Question 1: Linear Equations

Question: The sum of two numbers is 45. If one number is twice the other, find the larger number.

Solution:

Let the smaller number be x. The larger number is 2x.

Step 1: Form the equation.

x + 2x = 45

3x = 45

x = 45/3 = 15

Step 2: Calculate the larger number.

Larger Number = 2 * 15

= 30

Final Answer: 30.

Shortcut Method: Ratio Approach

The numbers are in the ratio 1:2.

Total parts = 1 + 2 = 3

Larger number = (2/3) * 45

= 30

Question 2: Quadratic Equations

Question: If the roots of x^2 - 7x + k = 0 are positive integers and one root is 3, find the other root and the value of k.

Solution:

Let the roots be 3 and a.

Step 1: Apply the sum of roots formula.

For the quadratic equation:

x^2 - 7x + k = 0

Sum of roots = 7

Therefore:

3 + a = 7

a = 7 - 3 = 4

Step 2: Apply the product of roots formula.

Product of roots = k

3 * 4 = k

k = 12

Final Answer: Other root = 4; k = 12.

Shortcut Method: Sum and Product of Roots

For the equation x^2 - Sx + P = 0:

• Sum of roots = S
• Product of roots = P

Other root = 7 - 3 = 4

k = 3 * 4 = 12

Question 3: Logarithms

Question: If log2 x = 5, find the value of log2(8x).

Solution:

Step 1: Convert the logarithmic equation into exponential form.

log2 x = 5

Therefore:

x = 2^5 = 32

Step 2: Calculate the required value.

Using the product rule of logarithms:

log2(8x) = log2 8 + log2 x

= 3 + 5

= 8

Final Answer: 8.

Shortcut Method: Logarithm Properties

Using the product rule:

logb(m * n) = logb m + logb n

Therefore:

log2(8x) = log2 8 + log2 x

= 3 + 5

= 8

CAT Geometry and Mensuration Questions with Solutions

Geometry and Mensuration cover triangles, circles, polygons, coordinate geometry, areas, volumes and surface areas. These questions test geometric properties, visualisation and formula application.

Question 1: Triangle Geometry

Question: A right-angled triangle has perpendicular sides measuring 6 cm and 8 cm. What is the length of its hypotenuse?

Solution:

Apply the Pythagoras theorem:

h^2 = a^2 + b^2

Substitute the given values:

h^2 = 6^2 + 8^2

h^2 = 36 + 64

h^2 = 100

h = sqrt(100) = 10 cm

Final Answer: 10 cm.

Shortcut Method: Pythagorean Triplet

The numbers 3, 4 and 5 form a standard Pythagorean triplet.

Multiplying each number by 2 gives:

6, 8 and 10.

Therefore, the hypotenuse is 10 cm.

Question 2: Circle Geometry

Question: A circle has a radius of 7 cm. Find its circumference and area. Use pi = 22/7.

Solution:

Step 1: Calculate the circumference.

Circumference:

C = 2 * pi * r

= 2 * (22/7) * 7

= 44 cm

Step 2: Calculate the area.

Area:

A = pi * r^2

= (22/7) * 7^2

= 22 * 7

= 154 cm^2

Final Answer: Circumference = 44 cm; Area = 154 cm^2.

Alternative Method: Relationship Between Area and Circumference

Aspirants can also calculate the area of a circle using:

A = (C * r)/2

= (44 * 7)/2

= 154 cm^2

Question 3: Mensuration

Question: A cylindrical tank has a radius of 7 m and a height of 10 m. Find its volume. Use pi = 22/7.

Solution:

Step 1: Apply the volume formula.

Volume of a cylinder:

V = pi * r^2 * h

Step 2: Substitute the values.

V = (22/7) * 7^2 * 10

= (22/7) * 49 * 10

Step 3: Simplify the expression.

V = 22 * 7 * 10

V = 1,540 m^3

Final Answer: 1,540 cubic metres.

Shortcut Method: Cancel Common Factors

Cancel 7 from 49 and the denominator before multiplying.

V = 22 * 7 * 10

= 1,540 m^3

CAT Number Systems and Modern Mathematics Questions

Number Systems covers divisibility, remainders, factors, LCM, HCF, digits and surds. Modern Mathematics covers permutations and combinations, probability, set theory, sequences and series.

Question 1: Number Systems

Question: Find the remainder when 2^30 is divided by 7.

Solution:

Step 1: Identify the remainder pattern.

Calculate the first few powers of 2 modulo 7:

2^1 = 2 (mod 7)

2^2 = 4 (mod 7)

2^3 = 1 (mod 7)

The remainder cycle is 2, 4, 1. It repeats after every three powers.

Step 2: Express the exponent as a multiple of 3.

30 = 3 * 10

Therefore:

2^30 = (2^3)^10

Since 2^3 leaves a remainder of 1 when divided by 7:

2^30 = 1^10 (mod 7)

Final Answer: The remainder is 1.

Shortcut Method: Cyclicity of Powers

The remainder cycle repeats after every three powers. Since 30 is divisible by 3, the remainder is 1.

Question 2: Permutations and Combinations

Question: In how many ways can 3 people be selected from 6 people?

Solution:

The question involves selection, so the order of selection does not matter. Apply the combination formula.

Step 1: Apply the formula.

nCr = n! / [r! * (n - r)!]

6C3 = 6! / (3! * 3!)

Step 2: Simplify.

6C3 = (6 * 5 * 4) / (3 * 2 * 1)

= 120/6

= 20

Final Answer: 20 ways.

Shortcut Method: Direct Calculation

6C3 = (6 * 5 * 4) / (3 * 2 * 1)

= 20

Question 3: Probability

Question: A bag contains 4 red balls and 6 blue balls. If one ball is drawn at random, what is the probability that it is red?

Solution:

Step 1: Calculate the total number of balls.

Total Balls = 4 + 6

= 10

Step 2: Identify favourable outcomes.

Favourable Outcomes = 4

Step 3: Apply the probability formula.

P(Red) = Favourable Outcomes / Total Outcomes

= 4/10

= 2/5

Final Answer: 2/5.

Shortcut Method: Direct Probability Calculation

P(Red) = 4/(4 + 6)

= 2/5

CAT Quant Formula Sheet and Shortcut Tricks PDF

A CAT Quant formula sheet and shortcut tricks PDF helps aspirants revise formulas and calculate faster. Regular practice also helps aspirants determine which formula or method suits a particular question.

Important CAT Quant Formulas

Topic	Formula
Percentage Change	(Change / Original Value) * 100
Profit Percentage	(Profit / Cost Price) * 100
Average	Sum of Values / Number of Values
Speed	Distance / Time
Work Rate	1 / Time Taken
Quadratic Roots	Sum = -b/a; Product = c/a
Circle Circumference	2 * pi * r
Circle Area	pi * r^2
Cylinder Volume	pi * r^2 * h
Probability	Favourable Outcomes / Total Outcomes
Combinations	nCr = n! / [r! * (n - r)!]

Important CAT Quant Shortcut Tricks

The following methods can reduce calculation time in CAT Quant questions:

• Percentage Multipliers: Multiply by 1.20 for a 20% increase and 0.80 for a 20% decrease. Aspirants can calculate successive percentage changes more easily using multipliers.
• Ratio-Based Methods: Apply ratios to profit and loss, mixtures, partnerships and comparison-based questions.
• LCM Approach: Use the LCM of individual completion times to calculate total work units in time-and-work questions.
• Inverse Proportionality: Apply the inverse relationship between speed and time when the distance remains constant.
• Divisibility Rules: Check divisibility before performing lengthy division in Number Systems questions.
• Cyclicity of Powers: Identify repeating remainder patterns to solve questions involving large exponents.
• Option Elimination: Remove incorrect options after narrowing down the possible answers.
• Simplified Calculations: Use symmetry, ratios and logical reasoning to reduce lengthy calculations.

How to Practise CAT Quantitative Aptitude Previous Year Questions

Solving CAT Quantitative Aptitude previous year questions with solutions requires regular practice and solution analysis. A structured approach helps aspirants identify weak topics, reduce calculation errors and improve accuracy.

1. Start with Topic-Wise Questions

Begin with Arithmetic PYQs, followed by Algebra, Geometry, Number Systems and Modern Mathematics. Practise related concepts together before moving to another topic.

For example, solve 15 to 20 questions on percentages and profit and loss in one practice session. Follow the same approach for ratios, time and work, and speed-distance questions.

2. Attempt Complete QA Sections

After covering the major topics, solve complete QA sections from previous CAT papers. Follow the original 40-minute time limit and avoid checking solutions during the attempt.

Record the following details after every practice session:

• Number of questions attempted.
• Number of correct and incorrect answers.
• Time spent on each question.
• Questions skipped due to difficulty.
• Questions affected by calculation errors.
• Topics that repeatedly cause delays.

The record helps aspirants identify whether the main difficulty lies in concept application, calculations or time management.

3. Analyse Solutions After Every Attempt

Checking the final answer is not enough. Examine the method used to solve each question and identify shorter approaches.

For example:

• In Arithmetic, check whether ratios or percentage multipliers reduce calculations.
• In Algebra, examine substitution and option elimination.
• In Geometry, identify whether a known property simplifies the solution.
• In Number Systems, look for divisibility rules and remainder patterns.

Compare the original approach with the alternative method. Practise the shorter approach only when it produces the correct result without unnecessary complexity.

4. Maintain a CAT Quant Error Log

An error log helps aspirants track recurring mistakes and plan revision sessions. Use the following format:

Column	Purpose
Topic	Identifies weak areas
Question Type	Shows recurring question patterns
Mistake Made	Reveals the cause of the error
Correct Approach	Records the appropriate solution method
Revision Date	Supports regular revision

Common Mistakes to Avoid in CAT Quantitative Aptitude

Several avoidable errors can affect performance in CAT Quant. Review the following points while practising previous-year questions:

• Attempting every question without checking its difficulty.
• Spending too much time on one lengthy calculation.
• Ignoring units, signs or decimal values.
• Applying formulas without checking their conditions.
• Skipping rough calculations when they are necessary.
• Neglecting Arithmetic, Number Systems or Modern Mathematics.
• Focusing on speed before developing accuracy.
• Making speculative MCQ attempts despite negative marking.
• Comparing raw scores across different CAT slots without considering normalisation.

Question selection is as important as mathematical accuracy. A lengthy question may not always be worth attempting when a simpler question remains unanswered.

CAT Quant Preparation Strategy

Use CAT Quantitative Aptitude previous year questions with solutions as a regular part of preparation. Start with Arithmetic and Algebra, then strengthen Geometry, Number Systems and Modern Mathematics.

A practical preparation sequence is:

1. Revise the fundamental concepts and formulas for each topic.
2. Solve topic-wise CAT Quant PYQs to practise different question formats.
3. Review incorrect answers and identify the reason for each mistake.
4. Prepare a formula sheet for regular revision.
5. Attempt complete QA sections under the 40-minute time limit.
6. Analyse mock tests to improve accuracy and question selection.
7. Revisit difficult questions and practise alternative solution methods.