Linear and Quadratic Equations

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Framing and solving equations forms the basis of quants. Get in as much practice as you can in these two topics because the spillover benefits from being good at framing equations can be enormous.
  1. Counting - Linear Equations

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

    1. 6
    2. 3
    3. 4
    4. More than 6
    • Correct AnswerChoice (D).
      More than 6.
      Correct answer
    • Explanatory Answer
    • Integer Values; Modulus
    • Medium
  2. Counting - Linear Equations

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

    1. 4
    2. 6
    3. 10
    4. 8
    • Correct AnswerChoice (C).
      10
      Correct answer
    • Explanatory Answer
    • Integer Values; Modulus
    • Medium
  3. Counting - Linear Equations

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

    1. 2
    2. 4
    3. 0
    4. 1
  4. Counting - Quadratic Equations

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

    1. 2
    2. 4
    3. 3
    4. 1
  5. Counting - Quadratic Equations

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

    1. 40
    2. 21
    3. 20
    4. 41
  6. 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
    • Correct AnswerChoice (D).
      More than 8.
      Correct answer
    • Explanatory Answer
    • Quadratics - Counting
    • Medium
  7. 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
  8. 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
    • Correct AnswerChoice (C).
      9.5
      Correct answer
    • Explanatory Answer
    • Linear Equations - Median
    • Medium
  9. 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. ;
    iii. a1, a2, a3 are integers; b1, b2, b3 are rational numbers, c1, c2, c3 are irrational numbers

    • Correct AnswerStatement i.
      Correct answer
    • Explanatory Answer
    • Condition for Unique Soln.
    • Hard
  10. Roots - Quadratic 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
  11. 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
    • Correct AnswerChoice (B).
      12 or 2
      Correct answer
    • Explanatory Answer
    • Sum and product of the roots
    • Easy
  12. Real and imaginary solutions for an equation

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

    1. 3
    2. 1
    3. 2
    4. none
    • Correct AnswerChoice (C).
      2
      Correct answer
    • Explanatory Answer
    • Real and imaginary solutions for an equation
    • Easy
  13. Value of the variables - Quadratic Equation

    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
  14. Progressions and Equations

    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
    • Correct AnswerChoice (B).
      9
      Correct answer
    • Explanatory Answer
    • AP and roots of an equation
    • Hard
  15. Roots of an Equation

    (3 + 2√2)(x2 - 3) + (3 - 2√2)(x2 - 3) = b which of the following can be one of the roots of the equation

    1. 2
    2. √2
    3. -√2
    4. All of the above
  16. 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 >= -5/4
    4. p <= 3/4
  17. Linear and Quadratic Expressions

    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 - x/2
    2. x/3 + 156
    3. 350 - x2/2
    4. x2 - 2x + 75
    • Correct AnswerChoice (A).
      Correct answer
    • Explanatory Answer
    • Linear and Quadratic Expressions
    • Medium

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