CAT Questions | CAT Algebra Questions | Linear Equations; Quadratic Equations

CAT Algebra questions from Linear equations and Quadratic equations that appear in the Quantitative Aptitude section of the CAT Exam consists of concepts from Equations and Algebra. Get as much practice as you can in these two topics because the benefits of being good at framing equations can be enormous and useful in other CAT topics as well. In CAT Exam, one can generally expect to get 1~2 questions from Linear Equations and Quadratic Equations. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. CAT Linear Equations - Counting

   3x + 4|y| = 33. How many integer values of (x, y) are possible?
   
   A. 6
   
   B. 3
   
   C. 4
   
   D. More than 6
   
   

   Correct Answer

   Choice D
   More than 6

   Explanation
   

   ---

2. CAT Linear Equations - Counting

   (|x| - 3) (|y| + 4) = 12. How many pairs of integers (x, y) satisfy this equation?
   
   A. 4
   
   B. 6
   
   C. 10
   
   D. 8
   
   

   Correct Answer

   Choice C
   10

   Explanation
   

   ---

3. CAT Linear Equations - Integer Values; Modulus

   x + |y| = 8, |x| + y = 6. How many pairs of x, y satisfy these two equations?
   
   A. 2
   
   B. 4
   
   C. 0
   
   D. 1
   
   

   Correct Answer

   Choice D
   1

   Explanation
   

   ---

4. CAT Quadratic Equations - Counting.

   What is the number of real solutions of the equation x² - 7|x| - 18 = 0?
   
   A. 2
   
   B. 4
   
   C. 3
   
   D. 1
   
   

   Correct Answer

   Choice A
   2

   Explanation
   

   ---

5. CAT Quadratic Equations - Counting

   x² - 9x + |k| = 0 has real roots. How many integer values can 'k' take?
   
   A. 40
   
   B. 21
   
   C. 20
   
   D. 41
   
   

   Correct Answer

   Choice D
   41

   Explanation

   ---

6. CAT Quadratic Equations - Integer Roots

   x² - 11x + |p| = 0 has integer roots. How many integer values can 'p' take?
   
   A. 6
   
   B. 4
   
   C. 8
   
   D. More than 8
   
   

   Correct Answer

   Choice D
   More than 8.

   Explanation

   ---

7. CAT Linear Equations - Integer Solutions

   2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation.
   
   A. 9
   
   B. 10
   
   C. 12
   
   D. 20
   
   

   Correct Answer

   Choice B
   10

   Explanation

   ---

8. CAT Linear Equations - Maximum, Minimum

   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.
   
   A. 11.5
   
   B. 9
   
   C. 9.5
   
   D. 12
   
   

   Correct Answer

   Choice C
   9.5

   Explanation

   ---

9. CAT Linear Equations - Unique Solutions

   a₁x + b₁y + c₁z = d₁, a₂x + b₂y + c₂z = d₂, a₃x + b₃y + c₃z = d₃.
   
   Which of the following statements if true would imply that the above system of equations does not have a unique solution?
   (i) = = ≠ (ii) = ; ≠
   
   A. Statement (i)
   
   B. Statement (ii)
   
   C. Statement (iii)
   
   D. None
   
   

   Correct Answer

   Statement i
   

   Explanation
   

   ---

10. CAT Quadratic Equations - Roots of Equation

    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.
    
    A. 6
    
    B. 0
    
    C. -16
    
    D. 2
    
    

    Correct Answer

    Choice C
    -16

    Explanation
    

    ---

11. CAT Quadratic Equations - Sum and product of the roots

    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?
    
    A. 6 or 3
    
    B. 12 or 2
    
    C. 8 or 4
    
    D. 12 or 4
    
    

    Correct Answer

    Choice B
    12 or 2

    Explanation
    

    ---

12. CAT Quadratic Equations - Real and imaginary Roots

    How many real solutions are there for the equation x² – 7|x| - 30 = 0?
    
    A. 3
    
    B. 1
    
    C. 2
    
    D. None
    
    

    Correct Answer

    Choice C
    2

    Explanation
    

    ---

13. CAT Quadratic Equations - Sum of the variables

    If (3x+2y-22)² + (4x-5y+9)² = 0 and 5x-4y = 0. Find the value of x+y.
    
    A. 7
    
    B. 9
    
    C. 11
    
    D. 13
    
    

    Correct Answer

    Choice B
    9

    Explanation
    

    ---

14. CAT Cubic Equations - AP and roots of an equation

    Let x³- x² + bx + c = 0 has 3 real roots which are in A.P. which of the following could be true
    
    A. b=2 , c=2
    
    B. b=1 , c=1
    
    C. b= -1 , c = 1
    
    D. b= -1 , c= -1
    
    

    Correct Answer

    Choice B
    b=1,c=1

    Explanation
    

    ---

15. CAT Linear Quadratic Equations - Roots of an Equation

    (3 + 2√2)^{(x2 - 3)} + (3 - 2√2)^{(x2 - 3)} = b which of the following can be the value of b?
    
    A. 2
    
    B. √2
    
    C. -√2
    
    D. All of the above
    
    

    Correct Answer

    Choice A
    2

    Explanation
    

    ---

16. CAT Quadratic Equations - Real roots

    If f(y) = x² + (2p + 1)x + p² - 1 and x is a real number, for what values of ‘p' the function becomes 0?
    
    A. p > 0
    
    B. p > -1
    
    C. p ≥
    
    D. p ≤
    
    

    Correct Answer

    Choice C
    p ≥ ^-5⁄₄

    Explanation
    

    ---

17. CAT Linear Quadratic Equations - Medium

    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 less articles a week. If the selling price of each article is Rs x, then which of the below expression represents the rupees a week the merchant will receive from the sales of the articles?
    
    A. 175 -
    
    B. + 156
    
    C. 350 -
    
    D. x² - 2x + 75
    
    

    Correct Answer

    Choice A
    175 - ^x⁄₂

    Explanation
    

    ---