CAT Questions | CAT Algebra Questions

CAT Quantitative Aptitude | CAT Algebra: 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?

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

  2. CAT Linear Equations - Counting

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

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

  3. CAT Linear Equations - Integer Values; Modulus

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

    1. 2
    2. 4
    3. 0
    4. 1
    Choice D
    1

  4. CAT Quadratic Equations - Counting.

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

    1. 2
    2. 4
    3. 3
    4. 1
    Choice A
    2

  5. CAT Quadratic Equations - Counting

    x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?

    1. 40
    2. 21
    3. 20
    4. 41
    Choice D
    41

  6. CAT Quadratic Equations - Integer Roots

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

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

  7. CAT Linear Equations - Integer Solutions

    2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation.

    1. 9
    2. 10
    3. 12
    4. 20
    Choice B
    10

  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.

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

  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. \\frac{a_{1}}{a_{2}}\\) = \\frac{b_{1}}{b_{2}}\\) = \\frac{c_{1}}{c_{2}}\\) ≠ \\frac{d_{1}}{d_{2}}\\)
    ii. \\frac{a_{1}}{a_{2}}\\) = \\frac{ a_{2} }{ a_{3} }\\) ; \\frac{ b_{1} }{ b_{2} }\\) = \\frac{ b_{2} }{ b_{3} }\\)
    iii. a1, a2, a3 are integers; b1, b2, b3 are rational numbers, c1, c2, c3 are irrational numbers

    1. Statement i
    2. Statement ii
    3. Statement iii
    4. None
    Statement i

  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.

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

  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?

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

  12. CAT Quadratic Equations - Real and imaginary Roots

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

    1. 3
    2. 1
    3. 2
    4. none
    Choice C
    2

  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.

    1. 7
    2. 9
    3. 11
    4. 13
    Choice B
    9

  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

    1. b=2,c=2
    2. b=1,c=1
    3. b= -1,c = 1
    4. b= -1,c= -1
    Choice B
    b=1,c=1

  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?

    1. 2
    2. √2
    3. -√2
    4. All of the above
    Choice A
    2

  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?

    1. p > 0
    2. p > -1
    3. p ≥ \\frac{-5}{4}\\)
    4. p ≤ \\frac{3}{4}\\)
    Choice C
    p ≥ \\frac{-5}{4}\\)

  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?

    1. 175 - \\frac{x}{2}\\)
    2. \\frac{x}{3}\\) + 156
    3. 350 - \\frac{x^2}{2}\\)
    4. x2 - 2x + 75
    Choice A
    175 - \\frac{x}{2}\\)

  18. The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below.

    IPMAT Rohtak Sample Paper Mock
    IPMAT Indore Sample Paper Mock

    Please note that the explanation button will take you to the IPMAT solution page.


  19. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Linear Equations

    One-fifth of a number is equal to \\frac{5}{8}\\)th of another number. If 35 is added to the first number, it becomes four times of the second number. Find the second number.

    1. 39
    2. 70
    3. 40
    4. 25
    Choice C
    40

  20. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Linear Equations

    John's present age is one fourth of his father's age two years ago. John's father's age will be twice Raman's age after 10 years. If Raman's 12th birthday was celebrated 2 years ago, then what is John's present age?

    1. 5 years
    2. 7 years
    3. 9 years
    4. 11 years
    Choice C
    9 years

The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.


  1. CAT 2017 Question Paper Slot 1 - Algebra

    If x + 1 = x2 and x > 0, then 2x4 is:

    1. 6 + 4√5
    2. 3 + 5√5
    3. 5 + 3√5
    4. 7 + 3√5
    Choice D
    7 + 3√5

  2. CAT 2017 Question Paper Slot 2 - Quadratic Equations

    The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

    1. 1
    2. 2
    3. 3
    4. 4
    Choice C
    3

  3. CAT 2018 Question Paper Slot 1 - Linear and Quadratic Equations

    If u2 + (u-2v-1)2 = -4v(u + v), then what is the value of u + 3v?

    1. \\frac{1}{4})
    2. \\frac{1}{2})
    3. 0
    4. -\\frac{1}{4})
    Choice D
    -\\frac{1}{4})

  4. CAT 2019 Question Paper Slot 1 - Quadratic equations

    The number of solutions of the equation |x|(6x2 + 1) = 5x2 is [TITA]

    5

  5. CAT 2019 Question Paper Slot 1 - Quadratic equations

    The product of the distinct roots of ∣x2 - x - 6∣ = x + 2 is

    1. -4
    2. -16
    3. -8
    4. -24
    Choice B
    -16

  6. CAT 2019 Question Paper Slot 2 - Linear & quadratic equations

    What is the largest positive integer such that \\frac{n^2+7n+12}{n^2-n-12}) is also positive integer?

    1. 6
    2. 8
    3. 16
    4. 12
    Choice D
    12

  7. CAT 2019 Question Paper Slot 2 - Linear & quadratic equations

    Let A be a real number. Then the roots of the equation x2 - 4x – log2A = 0 are real and distinct if and only if

    1. A < \\frac{1}{16})
    2. A > \\frac{1}{8})
    3. A > \\frac{1}{16})
    4. A < \\frac{1}{8})
    Choice C
    \\frac{1}{16})

  8. CAT 2019 Question Paper Slot 2 - Linear & quadratic equations

    The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?

    1. 3721
    2. 549
    3. 361
    4. 427
    Choice B
    549

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