Top 100 CAT Quant Questions 2025: Quantitative Aptitude

Preparing well for Quant is one of the biggest challenges in CAT. To help you, we have collected the most important CAT Quants questions that cover every key topic tested in the exam. 

By practicing these CAT quantitative aptitude questions and answers, you will build accuracy, speed, and confidence for the real test. 

CAT Quant Questions: Arithmtic

Below are the CAT arithmetic questions related to fractions, ratios, percentages, profit and loss, simple interest, compound interest, time and work, ages, etc.

Question 1:

If 1 is added to both the numerator and the denominator of a fraction, the resulting fraction is 3/4. If instead, 1 subtracted from both the numerator and the denominators of the fraction, the resulting fraction is 5/7. Find the original fraction.

Question 2:

Hulk is 3 times as old as his son. Five years later he shall be two and a half times as old as his son. How old is Hulk at present?

(A) 45
(B) 50
(C) 35
(D) 42

Question 3:

Let k be a constant. Find the condition for k so that the equations kx + y = 3 and 16x + ky = 4 have a unique solution.

Question 4:

The sum of the digits of a number consisting of three digits is 12. The middle digits is equal to half of the sum of other two. If the order of the digits, are reversed, the number is decreased by 198. Find the number.

Question 5:

The cost of 7 pencil, 10 erasers and 13 sharpeners is ₹114. The cost of 5 pencil, 7 erasers and 9 sharpeners is ₹80. Find the total cost of 1 pencil, 1 eraser and 1 sharpener.

Question 6:

A man divided 62500 among his four sons such that four times the share of his first son, three times the share of his second son, two times the share of his third son and the share of his fourth son are all equal. Find the share of each of his sons.

Question 7:

The ratio of the incomes of P and Q is 2 : 3. The ratio of their expenditures is 5 : 6. Who saves a greater part of his income?

(A)  P
(B)  Q
(C)  Both save equal parts of their incomes
(D)  Cannot say

Question 8:

If  p + qr=q + rp=p + rq= k find the sum of all the possible values of k.

(A) 1
(B) 2
(C) 0
(D) 3

Question 9:

x2 varies directly as y3 and when x = 6 , y = 3. Which of the following equations correctly represents the relationship between x and y?

(a). 6x² = 3y³   
(b). 3y² = 6x³
(c). 3x² = 2y³
(d). 3x² = 4y³

Question 10:

The value of gem stone varies as the square of its weight. The gem stone fell and broke into two pieces. The ratio between the weights of two pieces is 2 : 7. The loss occurred is Rs. 3080. Find the original price of gem stone.

(A) Rs. 5000
(B) Rs. 8000
(C) Rs. 8910
(D) Rs. 6060

Question 11:

Two numbers are respectively 20% and 50% more than a 3rd number. What is the percentage of 2nd with respect to 1^st?

(A) 125%
(B) 90%
(C) 80%
(D) 75%

Question 12:

In an election between two polled candidates P and Q, Q won the election by a majority of 40,000 votes. If P got 49% of the total votes, how many votes were totally polled? (Assume all the votes polled are valid)

(A) 20,00,000
(B) 10,00,000
(C) 40,00,000
(d) 25,00,000 

Question 13:

A student multiplied a number by  45  instead of  54 . What is the percentage error committed by the student?

(A) 36%
(B) 56.25%
(C) 30%
(D) 62.5%

Question 14:

Ravi and Kumar start a business with investments of ₹40,000 and ₹50,000 respectively. Kumar left the business after some time. If the profit sharing ratio at the end of the year is 8 : 5, the number of months after which Kumar left is ? 

Question 15:

Goyal and Gokul invest ₹20,000 and ₹30,000 respectively and start a business. Since Goyal manages the business, he gets a salary which is equal to 20% of the balance profit after deducting this salary. If Goyal’s total earnings are ₹4800 at the end of one year, what is the total profit made by the business?

(A) ₹4000
(B) ₹5200
(C) ₹9600
(D) ₹6400

Question 16:

Gopal purchases toffees at Rs. 10 per dozen and sells them at Rs. 12 for every 10 toffees. Find the gain percentage.

Question 17:

Amar sold a bike to Akbar at 20% loss. Akbar sold the bike to Anthony at 20% loss. The loss incurred by Akbar was ₹1,200 less than that incurred by Amar. Find the price at which Amar bought the bike 

Question 18:

Dhanna Seth bought a certain quantity of rice. He sold three-fifth of the rice at 12% profit and the rest at a 7% profit. Find the profit or loss in % he got in overall business. 

(A) 20% profit
(B) 15% loss
(C) 10% loss
(D) None of these 

Question 19:

A trader marked an article at (5x)% above the cost price. After giving a discount of (x + 5)%, he got a profit of (3x – 5)%. Find his profit percentage.

Question 20:

A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to

(A) 35
(B) 31
(C) 22
(D) 25

Question 21:

Spiderman invested Rs 50000 for 3 years at simple interest. If the rate of interest is 8%, 10% and 12% for the 1^st year, 2^nd year and 3^rd year respectively, find the interest earned by Spiderman

Question 22:

Sonalal lends ₹A, ₹B and ₹C to three of his friends, at 6% p.a. in simple interest. The interest amounts paid by the first second and the third friends at the end of the second year, fifth year and seventh year respectively are equal. 

Find A : B : C. 

Question 23:

Find the amount and compound interest on Rs 5000 for 2 years at 10%, interest being payable yearly.

Question 24:

A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

Question 25:

The difference between the compound interest and simple interest for two years on a sum of money is ₹160. If the simple interest is ₹2880 then interest rate in percent is:

(A) 5.55%
(B) 12.5%
(C) 11.11%
(D) 9%

More important resources for CAT exam:

What is CAT Exam?	CAT Eligibility Criteria
CAT Syllabus	CAT DILR Syllabus
CAT VARC Syllabus	CAT Answer Key
CAT Exam Analysis	CAT Percentile vs Score
CAT Admit Card	CAT Previous Year Question Papers
CAT Exam Pattern	CAT Practice Questions
Best books for CAT

CAT Quant Questions: Algebra

Below are the CAT algebra questions, related to equations, progressions, and inequalities:

Question 26:

Jamie Lannister borrows ₹2100 at the rate of 10% p.a. compounded annually and has to repay it in two equal annual instalments in 2 years. What is the value of each instalment?

Question 27:

Working alone, Raman takes 16 more days than the time taken by him and Sonu together to complete a job. Sonu, working alone, takes 36 more days than the time taken by him and Raman together to complete the job. Find the time taken by Sonu alone to complete the job.

Question 28:

A is 20% more efficient than B. If B can complete a piece of work in 30 days, then in how many days can both A and B complete the work working together?

(A) 11511
(B) 13711
(C) 15711
(D) 17511

Question 29:

Sachin and Tanuj can complete a piece of work in 32 days and 48 days respectively. If they work on alternate days, with Tanuj starting the work, in how many days will the work be completed?

Question 30:

A alone can do a piece of work in 6 days and B alone can do it in 8 days. A and B undertook some work for 1600 and completed it with the help of C in 3 days. How much of this amount will be paid to C?

(A) 375
(B) ₹200
(C) ₹500
(D) None of these

Question 31:

‘x’ number of men can finish a piece of work in 30 days. If there were 6 more men, the work could be finished in 10 days less. The original number of men was:

(A) 6
(B) 10
(C) 12
(D) 15

Question 32:

One man can complete a work in 129 days. One man starts the work and after that on each day one more man joins. With each man joining, the rate of work of every man doubles. In how many days does the work get completed?

Question 33:

Two pipes A and B can fill the tank in 40 and 60 minutes respectively. There is an outlet pipe C. If all the three pipes are opened simultaneously the tank is completely filled in 48 minutes. How much time will C take to empty the full tank?

(A) 20 minutes
(B) 30 minutes
(C) 40 minutes
(D) None of these

Question 34:

A pipe can empty a tank in 48 minutes. A second and a third pipe with diameters twice and four times as much as that of the first respectively, are also attached to the tank to empty it. The three pipes together can empty the tank in ______ (minutes).

Question 35:

John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?

Question 36:

A man drives a car at 40 km/h for 3 hours and at a speed of 60 km/h for next 4.5 hours. After that he finds that he has covered only 3/5^th of the total distance. At what speed he must travel the remaining distance to complete his entire journey in 10 hours.

(A) 104 km/h
(B) 165 km/h
(C) 100 km/h
(D) 162 km/h

Question 37:

A person covers a distance in following manner. He covers first half of the distance at 50 kmph, 40% of the remaining at 40 kmph and the remaining distance at 60 kmph. Find the average speed over the entire journey.

Question 38:

In covering a certain distance, the speed of A and B are in the ratio of 3: 4. A takes 30 minutes more than B to reach the destination. The time taken by B to reach the destination is:

(A) 1 hour
(B) 1.5 hours
(C) 2 hours
(D) 2.5 hours

Question 39:

Two persons A and B started from the same place and in the same direction. After 2 hours distance between them is observed to be 3.6 km. If the speed of the faster person rson is 2 m/s, find the speed of the slower person.

Question 40:

Raju and Baburao started simultaneously from towns P and Q respectively towards the starting point of the other. After crossing each other, Raju and Baburao took 36 minutes and 81 minutes respectively to reach their destinations. Find the time taken by them to cross each other.

Question 41:

A boat travels 63 km upstream in river and returns to its starting point. The time taken by the boat to travel upstream is two hours more than the time taken to travel downstream. The speed of the boat in still water is 8 times the speed of the stream. Find the speed of the stream.

Question 42:

Ant-Man started from a point on a lake in his sailboat and rowed in the same direction as the wind. He travelled 60 km in 6 hours and returned to his starting point after 10 more hours of rowing against the wind. If there were no wind, how long would he have taken for the entire trip?

Question 43:

In a race of 500 m, L beats M by 40 seconds and beats N by 125 m. If M and N run a 500 m race, M beats N by 40 seconds. Find the time taken (in seconds) by M to run the race.

(A) 160
(B) 240
(C) 280
(D) 320

Question 44:

Shizuka, Nobita and Doraemon start running simultaneously in the same direction from a point on a circular track of length 900 m. If their respective speeds are 3 m/s, 6 m/s and 9 m/s, after how much time will all three of them meet for the first time at the starting point?

Question 45:

The average age of 12 players of a team is 25 years. If the captain’s age is included, the average are increases by 1 year. The age of the captain is : 

(A) 25 yrs
(B) 38 yrs
(C) 36 yrs
(D) 26 yrs 

Question 46:

The average weight of 3 men A, B and C is 84 kg. Another man D joins the group, and the average now becomes 80 kg. If another man E, whose weight is 3 kg more than that of D, replaces A, then average weight of B, C, D and E becomes 79 kg. The weight of A is: 

(A) 70 kg
(B) 72 kg
(C) 75 kg
(D) 80 kg 

Question 47:

The average marks of classes A and B is 48, that of classes B and C is 72 and that of A and C is 60. Which of the following values are not possible for the average of all three classes together?

I. 48
II. 54
III. 59
IV. 72

(A) Only I and II
(B) Only I and IV
(C) Only I, II and IV
(D) Cannot be determined 

Explore additional free resources for CAT Exam:

Free CAT Mock Test PDF	CAT VARC Mock Test
CAT Quant Mock Test	CAT DILR Mock Test

CAT Quant Questions: Geometry & Mensuration

Let’s go through the top quantitative questions for CAT related to geometry and mesuration, covering triangles, trapezium, rhombus, circles, fields, and quadratics.

Question 48:

Six litres of a solution containing 20% alcohol are mixed with 4 litres of a solution containing 60% alcohol. Find the percentage of alcohol in the mixture.

(A) 80%
(B) 40%
(C) 36%
(D) 48%

Question 49:

A man purchased a TV set and a washing machine for a total of ₹75,000, and made an overall gain of 30% on selling both. If the profits on selling the TV set and the washing machine are 20% and 45% respectively, find the cost price of the washing machine.

Question 50:

In the figure, AB ││ CD  ││ EF. PQ and RS are the transversals cutting these parallel lines as shown. If  TU = 1.65, TV = 6.6 cm and WY = 6.4, then find XY = ? 

Question 51:

In a triangle PQR, ∠Q = 120º then which of the following is true- ?

(A) p² + r² =  q² − 2pr
(B) p² + r² = q² − pr
(C) p² + r² = q² + 2pr
(D) p² + r² = q² + pr

Question 52:

In the given figure,  ∆PQR ~ ∆ LMN. PX QR and LY MN.  If PQ = 3 cm and LM = 2 cm Then PXLY is 

(A). ¾
(B) ½
(C). 3/2
(D) None of these

Question 53:

The area of a trapezium is 768 cm, If parallel sides are in the ratio, 3:5 and perpendicular distance between them is 12 cm, then the sum of the parallel sides is?

(A). 144 cm.
(B). 64 cm.
(C). 8 cm.
(D). 128 cm.

Question 54:

Each side of a rhombus is equal to side of a square whose diagonal is 402 cm.  if the ratio of diagonals of rhombus are in the ratio 3:4, find it’s  area?

Question 55:

In the figure given below, PQ is diameter of the semicircle PQRS, center O , ∠SOR = 48° , If PR cuts SQ at X, calculate ∠PXS

(a). 50°
(b) 55° 
(c). 60°
(d) 66°

Question 56:

The base of triangular field is three times its altitude. If the cost of cultivating the field at 50 per hectare be 675, then its base and height are?

(A). 900m and 300m
(B). 600m and 300m
(C). 500m and 200m
(D). Can’t to be determined

Question 57:

The length of a rectangle is twice its breadth. If its length is decreased by 5cm and breadth is increase by 5cm, the area of the rectangle is increased by 75 cm² , then length of the rectangle is:

(A) 20 cm
(B) 30 cm
(D) 50 cm
(C) 40 cm

Question 58:

A vessel in the form of a hemisphere surmounted by a cylinder (open at the other end) of same radius is full of liquid whose volume is 432π cm³ . If water is filled in it to a level which is 1 cm below the top of vessel the volume of the water is 396 π cm³ . Find the height of the cylindrical part, 

(A. 6 cm
(B) 8 cm.
(C) 10 cm.
(D) 12 cm.

Question 59:

There is a square field whose side is 44 m. A square flower bed is prepared in its centre leaving a gravel path all around the flower bed. The total cost of laying the flower bed and gravelling path at ₹ 2.75 and ₹ 1.50 per square metre, respectively, is ₹ 4904. Find the width of the gravel path.

(A) 6 m
(B). 2 m
(C) 4 m
(D). 3 m

Question 60:

The roots of the quadratic equation 2x² – 7x + 2 = 0 are

(a). Rational and unequal
(b). Real and equal
(c). Imaginary
(d). Irrational   

CAT Quant Questions: Number System & Advanced Algebra

Below are the CAT quantitative aptitude questions related to number system and advanced algebra covering polynomials, remainder, AP, GP, logarithms, and series.

Question 61:

If α, β and γ are the roots of the equation x³ + 7x²  + 5x – 1 = 0, find   α  + β  + γ , αβ + βγ + γα  and αβγ. 

Question 62:

If x2+1×2-4x+1x+234=0 ，find x+1x.

Question 63:

Find the remainder when  x888  is divided by  x2-5x+6.

Question 64:

A person bought a certain number of oranges for ₹70. If the price of each orange was ₹ 2 less, he would have bought 4 more oranges for the same anount, the number of oranges he bought originally is

Question 65:

f(x) = │x – 7│ + │x – 10│. Find the minimum value of f(x) and also find the value (s) of x at which f(x) attains its minimum value.

Question 66:

Let x,  y,  z be three positive real numbers such that x – y = z – x and  xyz = 8. Find the minimum value of x.

Question 67:

How many solutions does the equation x2+x-9=9 have?

Question 69:

In an infinite GP, every term is 7 times the sum of all terms that follow. If sum of first and second terms is 9, find the GP.

Question 70:

Find the sum of infinite terms of the series  1+25+425+8125+……. 

(A) 5/4
(B) 3
(C) 3/2
(D) 5/3

Question 71:

Find the sum of   1+46+936+16216+251296+……∞ .

Question 72:

If fifth term of an AP is 10, what is the  sum up to nine term?

Question 73:

If the ratio of the sums up to n terms of the two arithmetic progressions is (7n+ 4) : (6n – 5), find the ratio of the 11^th terms of the two progressions

(A) 8161
(B) 7455
(C) 144115
(D) 151121

Question 74:

30+30+30..……∞

Question 75:

If (a5a)4a=(a44a)a4a,    (a≠1, 0,-1)^, . What is the value of a?

Question 76:

Arrange the following in ascending order : 21/3,31/4,41/5,51/6

Question 77:

If  7x=2y=14z, express  z in terms of x and y.

Question 78:

If (3.5)x=(0.35)y=1000, find the value of  1x-1y

Question 79:

Find the number of digits in 45150, given that log 5 =0.6990 and log 3 =0.4771.

Question 80:

Find the value of log 315 +2log 3 -5log 7 –  3 log 5. 

Question 81:

If 1a +1a +1a +1a + … +1 a =k2 , Find k. 

Practice with CAT PYQs:

CAT Previous Year Papers	CAT 2025 Question Paper
CAT 2024 Question Paper	CAT 2023 Question Paper
CAT 2022 Question Paper	CAT 2021 Question Paper
CAT 2020 Question Paper	CAT 2019 Question Paper

CAT Quantitative Aptitude Questions: Modern Math

In our series of top quant questions for CAT, the last set includes the modern math and higher math problems, covering number theory, permutations and combinations, probability basics, statistics, and coordinate geometry.

Question 81:

How many distinct prime factors does (2²²) (3³³) 555 (7⁷⁷) have?

Question 82:

If N=2a3b5c  how many numbers are less than N and are co-prime to it?

(A)  215N
(B) 415N
(D)  25N
(C) 815N

Question 83:

How many four-digit numbers are  perfect cubes also have an odd number of factors?

Question 84:

Find the unit digit of the expression 888^9235! +  222^9235! +  666^2359! + 999^9999!

Question 85:

How many zeros does 100! end with?

Question 86:

Find the sum of the remainders obtained when a number n is divided by 9 and 7 successively given that n is the smallest number that leaves remainders of 4, 6 and 9 when divided successively by 13, 11 and 15.

(A) 4
(B) 5
(C) 9
(D) 6

Question 87:

Joey has a certain number (less than 1000) of chocolates with him. If he distributes them equally among a group of 12 or 15 or 18 children, he would be left with 1 chocolate in each case. If he distributes the chocolates equally among 19 children, he would be left with no chocolates. How many chocolates does Joey have?

(A) 52
(B) 181
(C) 551
(D) 361

Question 88:

Find the largest number which divides 34, 58 and 94 leaving the same remainder in each case.

(A) 6
(B) 9
(C) 12
(D) 8

Question 89:

In a party there are 13 guests and each of them shakes hands with every other guest once. Find the total number of handshakes that were exchanged at the party.

Question 90:

Four athletes Messi, Ronaldo , Mbappe and Neymar participate in 6 athletic events. There is only one prize for  winning in each event and each of them won in at least one event. In how many ways could they have won the six prizes ?

Question 91:

If fx= 5×3+ 3×2+ x +1x+3×2+5×3  then f11f1/11+f12f1/12+…+f19f1/19 = ?

Question 92:

D (4, 5), E (2, 4) and F (6, – 1) are the mid points of the sides  BC, AC and AB of the  △ABC  respectively. Find the area of the △AEF.

Question 93:

Find the slope intercept form of the line joining the points (2, – 5) and (6, 3).

Question 94:

Find the value of sin43π8+cos43π8

Question 95:

A man looks up at a pole making angle of elevation  =  45° , When he looks at the reflection of the tip of the pole in water. He finds the angle of depression as 60° If the man is 1 m tall, find height of the pole.

Question 96:

If the centre of a circle is (3, 4) and 6x+8y+15=0 is a tangent to the circle, find the radius of the circle. 

Question 97:

If the lines 4x-3y+12=0, 4x-3y-8= 0 and 3x+4y+13=0 represent three sides of a square, find the equation of the fourth side.

Question 98:

You have a triangular field ABC in the shape of an equilateral triangle of side6 m. There is a 2m wide path around the field. Find the area of the path.

Question 99:

If the difference between the mode and the mean of a moderately symmetric. distribution is 42，find the difference between the mode and the median of. the distribution

Question 100:

Find the mean of the following data.

x	11	13	15	17	19
f	2	4	6	8	10

Download Answer Key of Above CAT Quants Questions

Click on the button below to download the answers of all these questions:

CAT Quantitative Aptitude Syllabus: Overview

Major Topic Area	Sub-Topics Covered	Importance in CAT
Arithmetic	Percentages, Profit & Loss, Ratio & Proportion, Averages, Mixtures, Time & Work, Time-Speed-Distance, Simple & Compound Interest	High weightage, appears every year
Algebra	Linear & Quadratic Equations, Inequalities, Functions, Progressions (AP, GP, HP), Logarithms	Moderate to high, concept-based
Geometry & Mensuration	Triangles, Circles, Polygons, Coordinate Geometry, Mensuration formulas	Consistently 4–6 questions
Number System	Divisibility, Factors, HCF & LCM, Remainders, Base System, Last Digit/Units Digit	Usually 2–3 questions
Modern Mathematics	Permutation & Combination, Probability, Set Theory, Statistics	Moderate weightage, slightly advanced

Tips to Solve CAT Quants Questions Effectively

1. Strengthen Your Basics First

Before trying shortcuts, make sure your concepts are clear. Focus on formulas, number properties, and standard problem types. A strong foundation will help you tackle even tricky CAT exam quantitative aptitude questions confidently. Without basics, accuracy and speed will always remain a challenge.

2. Practice Topic-Wise CAT Quant Questions

Break your preparation into smaller topics like Arithmetic, Algebra, Geometry, and Numbers. Solve at least 30–40 CAT Quant questions from each area before attempting full mocks. Topic-wise practice will give you clarity and help identify your strong and weak zones.

3. Solve Under Timed Conditions

CAT is not just about solving questions but solving them quickly. Always set a timer when practicing. Try finishing sets of 10–15 quantitative aptitude questions within a strict time frame. This habit will help you manage exam pressure and build speed effectively.

4. Learn and Apply Shortcuts

After mastering basics, learn Vedic maths tricks, approximation methods, and elimination strategies. Applying these in practice will help save valuable minutes in the exam. Remember, every second saved in the CAT Quant section can be used to attempt and secure more marks.

5. Analyze Your Mistakes Regularly

Don’t just practice—analyze. After every practice session or mock, revisit wrong attempts and understand why you went wrong. Was it a conceptual error, a silly mistake, or a time issue? Identifying this will sharpen your approach and reduce errors in future CAT exam questions.

6. Take Sectional Tests and Mocks

Once you are comfortable with individual topics, start taking sectional tests and full-length mocks. They simulate real exam pressure and help you discover new weak areas. Regular exposure to timed environments is the best way to master the CAT exam quantitative aptitude questions.

FAQs About CAT Quant Questions

India’s Top CAT/MBA Prep Programs:

• Online CAT Coaching
• Online XAT Coaching
• Online SNAP Coaching
• Online OMET Coaching

Best Offline Coaching Programs for CAT:

CAT Coaching in Jaipur	CAT Coaching in Indore
CAT Coaching in Mumbai	CAT Coaching in Bhopal
CAT Coaching in Jodhpur	CAT Coaching in Gwalior
CAT Coaching in Nagpur