Quantitative Aptitude: Quadratic Equations Set 5

Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly.
 

  1. I. 3x2 + 22 x + 24 = 0
    II. 2y2 + 11y + 12 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option E
    Solution:

    3x2 + 22 x + 24 = 0
    3x2 + 18x + 4x + 24 = 0
    Gives x = -4/3, -6
    2y2 + 11y + 12 = 0
    2y2 + 8y + 3y + 12 = 0
    Gives y = -4, -3/2
    Put all values on number line and analyze the relationship
    -6…..-4…. -3/2….-4/3
  2. I. 20x2 – 31x + 12 = 0
    II. 4y2 + 5y – 6 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option C
    Solution:

    20x2 – 31x + 12 = 0
    20x2 – 16x – 15x + 12 = 0
    Gives x = 3/4, 4/5
    4y2 + 5y – 6 = 0
    4y2 + 5y – 6 = 0
    Gives y = -2, 3/4
    Put all values on number line and analyze the relationship
    -2…. 3/4… 4/5
  3. I. 3x2 + 14x – 5 = 0
    II. 4y2 + 5y – 6 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option E
    Solution:

    3x2 + 14x – 5 = 0
    3x2 + 15x – x – 5 = 0
    Gives x = -5, 1/3
    4y2 + 5y – 6 = 0
    4y2 + 5y – 6 = 0
    Gives y = -2, 3/4
    Put all values on number line and analyze the relationship
    -5….-2….. 1/3…. 3/4
  4. I. 2x2 – 15x + 7 = 0
    II. 8y2 + 6y – 5 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option C
    Solution:

    2x2 – 15x + 7 = 0
    2x2 – 14x – x + 7 = 0
    Gives x = 1/2, 7
    8y2 + 6y – 5 = 0
    8y2 – 4y + 10y – 5 = 0
    Gives y = -5/4, 1/2
    Put all values on number line and analyze the relationship
    -5/4…. 1/2 …. 7
  5. I. 3x2 + 16x + 20 = 0
    II. 3y2 – 14y – 5 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option B
    Solution:

    3x2 + 16x + 20 = 0
    3x2 + 6x + 10x + 20 = 0
    Gives x = -2, -10/3
    3y2 – 14y – 5 = 0
    3y2 – 15y + y – 5 = 0
    Gives y = -1/3, 5
    Put all values on number line and analyze the relationship
    -10/3… -2…. -1/3…. 5
  6. I. 3x2 + 7x – 6 = 0
    II. 6y2 – 35y + 50 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option B
    Solution:

    3x2 + 7x – 6 = 0
    3x2 + 9x – 2x – 6 = 0
    Gives x = -3, 2/3
    6y2 – 35y + 50 = 0
    6y2 – 15y – 20y + 50 = 0
    Gives y = 5/2, 10/3
    Put all values on number line and analyze the relationship
    -3… 2/3… 5/2…. 10/3
  7. I. 7x2 – 11x – 6 = 0
    II. 6y2 + 13y + 5 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option A
    Solution:

    7x2 – 11x – 6 = 0
    7x2 – 14x + 3x – 6 = 0
    Gives x = -3/7, 2
    6y2 + 13y + 5 = 0
    6y2 + 3y + 10y + 5 = 0
    Gives y = -5/3, -1/2
    Put all values on number line and analyze the relationship
    -5/3…. -1/2…. -3/7….. 2
  8. I. 3x2 + 4x – 39 = 0
    II. 3y2 – 5y – 78 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option E
    Solution:

    3x2 + 4x – 39 = 0
    3x2 – 9x + 13x – 39 = 0
    Gives x = -13/3, 3
    3y2 – 5y – 78 = 0
    3y2 – 18y + 13y – 78 = 0
    Gives y = -13/3, 6
    Put all values on number line and analyze the relationship
    -13/3…. 3…. 6
  9. I. 4x2 + 13x + 9 = 0
    II. 3y2 – 7y – 20 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option E
    Solution:

    4x2 + 13x + 9 = 0
    4x2 + 4x + 9x + 9 = 0
    Gives x = -9/4, -1
    3y2 – 7y – 20 = 0
    3y2 – 12y + 5y – 20 = 0
    Gives y = -5/3, 4
    Put all values on number line and analyze the relationship
    -9/4…. -5/3…. -1….4
  10. I. 4x2 + 13x + 10 = 0
    II. 4y2 – 7y – 15 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option D
    Solution:

    4x2 + 13x + 10 = 0
    4x2 + 8x + 5x + 10 = 0
    Gives x = -2, -5/4
    4y2 – 7y – 15 = 0
    4y2 – 12y + 5y – 15 = 0
    Gives y = -5/4, 3
    Put all values on number line and analyze the relationship
    -2… -5/4…. 3

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