Algebra Questions for the CAT are part of the Quantitative Aptitude section in the CAT exam. Through algebra questions, aspirants are tested on concepts related to Linear Equations, Quadratic Equations, Inequalities, Logarithm, and Functions. The difficulty level of the Algebra questions can be easy to moderate.

## Boolean Algebra Rules for the CAT Exam

**1.** Commutative Law

**2. **Associative Law

**3. **Distributive Law

**4.** AND Law

**5.** OR Law

**6**. Inversion Law.

## Algebra Identities for the CAT Exam

## Algebra Tricks for the CAT Exam

- Do exercises and solve problems regularly to improve algebra skills
- Be organized with your answers. Write in a neat way so that you don't get confused with the numbers and formulas
- Learn from the mistakes and understand them so that they can be avoided
- Use different methods to solve the same problems to get the accurate results
- Solve questions by substitution or elimination to solve systems of equations

## What are some CAT level Algebra Practice Questions?

**Q 1.** If the real root of the cubic equation 8a 3− 12a 2−6a−1 = 0 is expressed as (p 1/3 +q 1/3+1)/r where p, q, r are natural numbers, what is the value of p + q + r?

**Answer: **8

**Q 2. **In how many ways can a pair of integers (x , a) be chosen such that x^2 − 2âˆ£xâˆ£ + âˆ£a−2âˆ£= 0?

A. 6

B. 5

C. 4

D. 7

**Answer: **D

**Q 3. **The number of pairs of integers (x, y) satisfying x ≥ y ≥ −20 and 2x + 5y = 99

**Answer: **17

**Q 4.** The value of loga( b ) + a logb( a ), for 1 < a ≤ b cannot be equal to

A. 0

B. -1

C. 1

D. -0.5

**Answer:** C

**Q 5.** Let f(x) = x 2 + ax + b and g(x) = f(x + 1) − f(x − 1) f(x) ≥ 0 . If for all real x, and g(20) = 72. then the smallest possible value of b is

A. 16

B. 4

C. 1

D. 0

**Answer:** B

**Q 6. **If f(x + y) = f(x)f(y) f(5) = 4 and , then f(10) − f(−10) is equal to

A. 14.0625

B. 0

C. 15.9375

D. 3

**Answer:** C

## What are the must-do algebra questions for the CAT exam?

**Q 7.** How many pairs(a, b) of positive integers are there such that a ≤ b and ab = 4^2017?

A. 2018

B. 2019

C. 2017

D. 2020

**Answer:** A

**Q 8.** If f(5 + x) = f(5 − x) for every real x, and f(x) = 0 has four distinct real roots, then the sum of these roots is

A. 0

B. 40

C. 10

D. 20

**Answer:** D

**Q 9.** If log4 5 = (log4y)(log65^(1/2)), then y equals

**Answer:**36

**Q 10.** The area of the region satisfying the inequalities âˆ£ x âˆ£ −y ≤ 1, y ≥ 0 and y ≤ 1 is

**Answer:**3

**Q 11.** How many distinct positive integer-valued solutions exist to the equation (X 2 − 7x + 11) (X −13x+42) =?

A. 8

B. 4

C. 2

D. 6

**Answer: **D

## What were the previous year CAT algebra questions?

**Q 12.** If the real root of the cubic equation 8a 3− 12a 2−6a−1 = 0 is expressed as (p 1/3 +q 1/3+1)/r where p, q, r are natural numbers, what is the value of p + q + r?

**Answer**: 8

**Q 13**. The value of loga( b ) + a logb( a ), for 1 < a ≤ b cannot be equal to

A. 0

B. -1

C. 1

D. -0.5

**Answer**: C

**Q 14 **If f(x + y) = f(x)f(y) f(5) = 4 and , then f(10) − f(−10) is equal to

A. 14.0625

B. 0

C. 15.9375

D. 3

**Answer**: C

## What were the algebra questions on the CAT 2022 exam?

**Q 15.** Let a and b be natural numbers. If a 2 + ab + a = 14 and b 2 + ab + b = 28, then (2a + b) equals

A. 10

B. 7

C. 8

D. 9

**Answer:** C

**Q 16.** For natural numbers x,y, and z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is

**Answer:**34

**Q 17.** The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

A. 3

B. 1

C. 4

D. 5

**Answer: **D

**Q 18.**The number of pairs of integers (x , y) satisfying x > y > 20 and 2x 5x 99 is

**Answer**: 17

**Q 19. **In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

A. 4

B. 3

C. 5

D. 6

**Answer**: A

## What were the algebra questions on the CAT 2021 exam?

**Q 20.** If Y is a negative number such that, then Y equals to:

A. log2(1/5)

B. log2 (1/3)

C. -log2(1/5)

D. -log2(1/3)

**Answer**: B

**Q 21.** Fn is defined as the set {2n + 6, 3n + 5 } where n is a natural number less than or equal to 500. For how many values of n will Fn and Fn+1 have one element each which is divisible by 7?

**Answer: **72

**Q 22**. For a cubic function f(x), f(1)=f(2)=f(3)=2 and f(4)=14, then find the value of f(5)

**Answer**: 50

**Q 23.** For all real values of x and y, f(x+y) = f(x)+f(y). If f(3)+f(4)+f(5)+............f(11) = 189, then find the value of f(15).

A. 15

B. 45

C. 90

D. 60

**Answer:** B

**Q 24.** Find the number of consecutive zeros after the decimal in the number 1/40 34, given that log2=0.3010

**Answer**: 54

## What were the algebra questions on the CAT 2020 exam?

**Q 25.**For the given pair (x, y) of positive integers, such that 4x-17y=1 and x<1000 how many integer values of y satisfy the given conditions?

A. 56

B. 57

C. 58

D. 59

**Answer:** Option D

**Q 26.** One year's payment to the servant is Rs. 90 plus one turban. The servant leaves after 9 months and receives Rs. 65 and a turban. Then find the price of the turban

A. Rs.10

B. Rs.15

C. Rs.7.5

D. Cannot be determined

**Answer:** Option (A)

**Q 27**. How many integer solutions exist for the equation 11x + 15y = -1 such that both x and y are less than 100?

A. 15

B. 16

C. 17

D. 18

**Answer**: Option (B)

**Q 28.** What are the number of integral solutions of the equation 7x + 3y = 123 for x,y > 0

A. 3

B. 5

C. 12

D. Infinite

**Answer:** Option (B)

**Q 29. **If log4 5 = (log4y)(log65^(1/2)), then y equals

**Answer**: 36

## What are some CAT Average questions?

**Average questions** are questions where aspirants are tested on concepts related to Formulas, and Permutations.

**Q 30.** The average monthly income of P and Q is 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is 5200. The monthly income of P is

(a) 3500

(b) 4000

(c) 4050

(d) 5000

**Answer: **B

**Q 31. **Average age of ten persons learning yoga is 32 years. When the age of their instructor is added, the average age becomes 34 years. The age of their instructor is

(a) 46 years

(b) 52 years

(c) 54 years

(d) 56 years

**Answer: **C

**Q 32. **The average monthly income of a family of four earning members was ` 15130. One of the daughters in the family got married and left home, so the average monthly income of the family came down to 14660. What is the monthly income of the married daughter?

(a) 12000

(b) 15350

(c) 16540

(d) Cannot be determined

(e) None of these

**Answer:** C

**Q 33**. The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is

(a) 45 kg

(b) 50 kg

(c) 53 kg

(d) 55 kg

**Answer**: C

**Q 34**. The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?

(a) 40 years

(b) 42 years

(c) 48 years

(d) 50 years

**Answer:** B

## What are some CAT Arithmetic questions?

**Arithmetic Questions** are typically tested on concepts related to Formula and divisibility. The difficulty level of the Algebra questions can be easy to moderate..

**Q 35. **Ravi invests a sum of money in a bank which gives a simple interest of 5% p.a. He invests twice the amount of money in another bank which gives an interest of 3% P..A. compounded annually. At the end of 3 years, the interest earned from which bank would be higher and by what percent(approx)?

A. 1st, 25%

B. 2nd, 10%

C. 2nd, 24%

D. 1st. 15%

**Answer. **C

**Q 36. ** On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

**Answer:** 3 π (5+(12/π))

**Q 37.** A solid right circular cone of height 27 cm is cut into two pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

A. 243

B. 232

C. 256

D. 264

**Answer**: A

**Q 38**. If the volume of a right circular cylinder that can be cut out from a sphere of radius 6 cm is the maximum possible, then find the radius of the cylinder.

**Answer**: 26

## Which Book or Study Material is best for Quant in CAT Exam?

The best book for Quant which mostly students opt for is Arun Sharma's CAT books. The particular book for Quantitative Aptitude is "How to Prepare for Quantitative Aptitude for CAT". These books are published by the renowned publisher McGraw Hill Education (India) Private Limited.

If you are looking for other study materials, mock tests, and books for practice then you can check R.S. Aggarwal, S.Chand, and Aashish Arora too.

## How to Prepare for Quantitative Aptitude for CAT?

Here are some tips to prepare for Quantitative Aptitude for the CAT exam:

- Maintain your speed
- Solve Practice Questions
- Learn formulas and Concepts as much as you can
- Break the question into small parts
- Stay Organized

## How to prepare for Reading Comprehension for CAT?

- Maintain a calm and focused mindset while solving the VARC section. Stress and anxiety can slow you down and affect your comprehension
- Set a time limit for each passage and stick to it. If you find yourself spending too much time on a single question, move on and come back to it later if time permits.
- Don't draw your own conclusions! While (B) may seem like a plausible situation, the passage never mentions it.
- Always pay attention to dates and time periods when mentioned in questions, particularly in natural science passages.
- Develop a habit of reading newspapers, magazines, online articles, and various genres of literature. This will improve your reading speed, comprehension skills, and vocabulary.

## Where can I find a PDF containing algebra questions along with their solutions?

Get Algebra Questions and Answers PDF - Download Now

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