CAT Algebra Questions 2025: Topics, Books, Preparation Tips

CAT Algebra questions 2025 comprises questions based on linear and quadratic equations, real and imaginary numbers, quadratic equations, inequalities, basic algebraic formulae, finding out roots, maxima and minima, and many other topics. Students preparing for the CAT exam need not worry about the algebra section, which comprises basic algebraic formulas.

CAT Algebra Questions 2025

The table below comprises CAT Algebra questions 2025, which are gathered from actual CAT question papers and mock question papers. You can refer to the CAT algebra questions below for their practice.

Ques 1. In ABC the medians AD, BE and CF meet at G. The coordinates of A, B, and G are (4, 7), (2, 3), and (4, 5) respectively. Find the length of the median CF.

Options: 

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

Ques 2. 3x + 4|y| = 33. How many integer values of (x, y) are possible?

Options: 

1. 6
2. 3
3. 4
4. More than 6

Ques 3. A change-making machine contains one-rupee, two-rupee and five-rupee coins. The total number of coins is 300.

The amount is Rs. 96. If the numbers of one-rupee coins and two-rupee coins are interchanges, the value comes down by Rs. 40.

The total number of five-rupee coin is:

Options: 

1. 100
2. 140
3. 60
4. 150

Ques 4. If | r – 6 | = 11 and | 2q – 12 | = 8, what is the minimum possible value of q / r?

Options: 

1. -2/5
2. 2/17
3. 10/17
4. None of the above

Ques 5. (|x| - 3) (|y| + 4) = 12. How many pairs of integers (x, y) satisfy this equation?

Options: 

1. 4
2. 6
3. 10
4. 8

Also Read: Is CAT Exam Tough?

Ques 6. x + |y| = 8, |x| + y = 6. How many pairs of x, y satisfy these two equations?

Options: 

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

Ques 7. What is the number of real solutions of the equation x2 - 7|x| - 18 = 0?

Options: 

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

Ques 8. x2 - 11x + |p| = 0 has integer roots. How many integer values can 'p' take?

Options: 

1. 6
2. 4
3. 8
4. More than 8

Ques 9. Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Median (a,b,c) - Mean (a,b,c) = 2. Find the median of a, b, and c.

Also Read: CAT Geometry Questions

Options: 

1. 11.5
2. 9
3. 9.5
4. 12

Ques 10. Equation x2 + 5x – 7 = 0 has roots a and b. Equation 2x2 + px + q = 0 has roots a + 1 and b + 1. Find p + q.

Options: 

1. 6
2. 0
3. -16
4. 2

Ques 11. How many real solutions are there for the equation x2 – 7|x| - 30 = 0?

Options: 

1. 3
2. 1
3. 2
4. None of the above

Ques 12. Sum of the roots of a quadratic equation is 5 less than the product of the roots. If one root is 1 more than the other root, find the product of the roots?

Options: 

1. 6 or 3
2. 12 or 2
3. 8 or 4
4. 12 or 4

Ques 13. (3 + 2√2)(x2 - 3) + (3 - 2√2)(x2 - 3) = b which of the following can be the value of b?

Options: 

1. 2
2. √2
3. -√2
4. All of the above

Ques 14. If f(y) = x2 + (2p + 1)x + p2 - 1 and  x is a real number, for what values of ‘p' the function becomes 0?

Options: 

1. p > 0
2. p > -1
3. p ≥ −54
4. p ≤  34

Also Read: CAT Exam Day Guidelines

Ques 15. Let a,b,c be non-zero real numbers such that b2<4ac, and f(x)=ax2+bx+c. If the set S consists of al integers m such that f(m)<0, then the set S must necessarily be:

Options: 

1. the set of all integers
2. either the empty set or the set of all integers
3. the empty set
4. the set of all positive integers

Ques 16. If 3x+2|y|+y=7 and x+|x|+3y=1, then x+2y is

Options: 

1. 0
2. 1
3. −43
4. 83

Ques 17. A merchant decides to sell off 100 articles a week at a selling price of Rs. 150 each.

For each 4% rise in the selling price, he sells 3 fewer articles a week.

If the selling price of each article is Rs x, then which of the below expressions represents the number of articles sold by the merchant in that week?

Options: 

1. 175 - x2
2. x3
3.  + 156
4. 350 - x22
5. x2 - 2x + 75

CAT Algebra Topics

In the Quantitative Aptitude of Common Admission Test (CAT), Algebra is one of the sub-sections. You can check out the topics of CAT algebra for your reference:

• Basics Algebraic Formulae
• Finding out roots
• Maxima and Minima
• Higher Degree Equations
• Descartes Rule of Signs
• Linear Equations
• Problems on Ages
• Functions
• Modifications of graphs
• The smallest value in a maximum function
• Number of Integer solutions
• Quadratic Equations
• Inequalities
• Logarithm

CAT Quantitative Aptitude Books

Students preparing for CAT are always advised to to cover practice books to understand the concept and question patterns. The table below contains Quantitative Aptitude books for the CAT exam which will cover the Algebra section as well.

CAT Algebra Preparation Tips

You are advised to refer to the books mentioned in the table above. Apart from solving practice books, below is a list of tips for CAT Algebra preparation:

• When it comes to preparing for the CAT Algebra topic, it is advised to prepare for the complete section of CAT Quantitative Aptitude as it will increase the chances of better performance in the exam.
• Calculators are usually not allowed in the exam. Hence, the candidates should practice calculation without relying on calculators. Blank sheets will be provided at the examination for rough work.
• Learning about Mathematical values such as Square, Cube, Root, and Square Roots can lead to faster ways of solving questions.
• You are advised to attempt multiple mock tests and practice as many CAT Algebra questions as possible.

Also Read: How to Crack CAT Exam?