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}\\)

CAT Online Preparation | CAT Algebra Videos On YouTube


Other useful sources for Algebra Questions | Linear Quadratic Sample Questions



CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com