CAT Quantitative Aptitude Questions can be solved directly with the right knowledge of formulas and some tricks. In CAT 2021 candidates will be asked both MCQ and TITA type questions from the Quantitative Aptitude section. Based on CAT Quant Paper Analysis of the last year, the questions are asked from topics like Arithmetic, Algebra, Logarithms, Number System, Functions, Geometry, and Mensuration. Check CAT Quantitative Aptitude Syllabus

Read the article to check the previous year’s solved sample questions from CAT quantitative aptitude section. Candidates can solve these questions to prepare for the exam. 

CAT QA Solved Questions

Q1- If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

1. 0
2. 40
3. 10
4. 20

ANS:- D. 20

Q2- A train travelled at 1/3 of its usual speed, and reached the destination 30 minutes after the scheduled time. During the return journey, the train travelled at its usual speed for 5 minutes. At that time the train had also stopped for 4 minutes for an emergency. By what % the train must now increase its usual speed so as to reach the destination at the scheduled time?

1. 58
2. 67
3. 50
4. 61

ANS:- B.67

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Q3- What is the number of real value solutions of the equation 2x + 2-x = 2 - (x - 2)2 is

1. infinite
2. 0
3. 1
4. 2

ANS:- B.0

Q4- Points A and B connect the straight road. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. When they met each other, they took 45 & 20 minutes, respectively, to complete their journeys. What will be the speed of Car 2, in km/hr, if Car 1 travels at the speed of 60 km/hr?

1. 90
2. 80
3. 70
4. 100

ANS:- A. 90

Q5- Let us consider that A, B, and C are three positive integers. The sum of A & the mean of B and C is 5. Also, the sum of B & the mean of A and C is 7. What is the sum of A and B?

1. 6
2. 4
3. 7
4. 5

ANS:- A. 6

Q6- The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is

1. 5544
2. 4466
3. 4864
4. 5050

ANS:- A. 5544

Q7- Among 100 students, x1 have birthdays in January, x2 have birthdays in February, and so on. What will be the smallest possible value of x0 if x0 = max(x1, x2, ..., x12)?

1. 8
2. 10
3. 12
4. 9

ANS:- D. 9

Q8- There are 2 persons who are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. One more train is there that came from behind them and crossed them in 90 and 100 seconds, respectively. What will be the time taken by the train to cross an electric post?

1. 87
2. 82
3. 78
4. 75

ANS:- B. 82

Q9- How many distinct positive integer-valued solutions exist to the equation (x2 - 7x + 11)(x2 - 13x + 42) = 1?

1. 6
2. 2
3. 4
4. 8

ANS:- A. 6

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Q10- If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

1. 56
2. 49
3. 46
4. 59

ANS:- C. 46

Q11- If y is a negative number such that 2y2log35 = 5log23, then y equals

1. log2 (1/3)
2. log2 (1/5)
3. −log2 (1/3)
4. −log2 (1/5)

ANS:- A. log2 (1/3)

Q12- Let us consider that an alloy is prepared by mixing metals A, B, C in the proportion 3: 4: 7 by volume. Weights of A, B, C are in the ratio 5: 2: 6. In 130 kg of the alloy, what will be the weight of metal C?

1. 84
2. 48
3. 96
4. 70

ANS:- A. 84

Q13- Let us consider that in a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. What will be the distance over which the race has been conducted?

1. 550
2. 475
3. 500
4. 450

ANS:- D. 450

Q14- The value of logaa/b + logbb/a, for 1 < a ≤ b cannot be equal to

1. -0.5
2. 1
3. 0
4. -1

ANS:- B. 1

Q15- Let us consider that C is a circle. The radius of circle C is 5 meters and the center is O. Also let us consider that PQ is a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. What will be the length of PQ?

1. 6.6
2. 7.2
3. 8.8
4. 7.8

ANS:- C. 8.8

Read More How to Prepare for CAT Algebra?

Q16- In a college, students have to choose at least 2 subjects from chemistry, mathematics, and physics. A total of 18 students have choosing all three subjects, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. What will be the smallest possible number of students who could choose chemistry as one of their subjects?

1. 22
2. 19
3. 20
4. 21

ANS:- C. 20

Q17- Let f(x) = x2 + ax + b and g(x) = f(x + 1) - f(x - 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is

1. 16
2. 1
3. 4
4. 0

ANS:- C. 4

Q18- The sum of perimeters of an equilateral triangle and a rectangle is 90 cm. The area, T, of the triangle and the area, R, of the rectangle, both in sq cm, satisfy the relationship R = T2. What will be the length, in cm, of the longer side of the rectangle, if the sides of the rectangle are in the ratio 1: 3?

1. 27
2. 18
3. 21
4. 24

ANS:- A. 27

Read More How to Prepare for CAT Arithmetic?

Q19- What is the number of integers that satisfy the equality (x2 - 5x + 7)x + 1 = 1 is

1. 5
2. 4
3. 3
4. 2

ANS:- C. 3

Q20- In how many ways can a pair of integers (x , a) be chosen such that x2 − 2 | x | + | a - 2 | = 0 ?

1. 7
2. 6
3. 4
4. 5

ANS:- A. 7

Quick Links

1. CAT Previous Year Question Papers of VARC
2. CAT Previous Year Question Papers of DILR