Quantitative Aptitude: Quadratic Equations Set 7

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 – 17x + 10 = 0
    II. 3y2 + 4y – 4 = 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:

    3x2 – 17x + 10 = 0
    3x2 – 15x – 2x + 10 = 0
    Gives x = 2/3, 5
    3y2 + 4y – 4 = 0
    3y2 + 6y – 2y – 4 = 0
    Gives y = -2, 2/3
    Put all values on number line and analyze the relationship
    -2…. 2/3…… 5
  2. I. 3x2 – 14x + 8 = 0
    II. 3y2 – 20y + 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 – 14x +8 = 0
    3x2 – 12x – 2x + 8 = 0
    Gives x = 2/3, 4
    3y2 – 20y + 12 = 0
    3y2 – 18y – 2y + 12 = 0
    Gives y = 6, 2/3
    Put all values on number line and analyze the relationship
    2/3….. 4….. 6
  3. I. 3x2 – 19x + 28 = 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 A
    Solution:

    4x2 – 19x + 28 = 0
    4x2 – 12x – 7x + 28 = 0
    Gives x = 7/3, 4
    4y2 – 5y – 6 = 0
    4y2 – 8y + 3y – 6 = 0
    Gives y = -3/4, 2
    Put all values on number line and analyze the relationship
    -3/4…… 2…… 7/3…. 4
  4. I. 6x2 + 23x + 21 = 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:

    6x2 + 23x + 21 = 0
    6x2 + 9x + 14x + 21 = 0
    Gives x = -7/3, -3/2
    3y2 – 14y – 5 = 0
    3y2 – 15y + y – 5 = 0
    Gives y = -1/3, 5
    Put all values on number line and analyze the relationship
    -7/3…… -3/2….. -1/3…… 5
  5. I. 2x2 – 7x + 3 = 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 A
    Solution:

    2x2 – 7x + 3 = 0
    2x2 – 6x – x + 3 = 0
    Gives x = 3, 1/2
    2y2 + 11y + 12 = 0
    2y2 + 8y + 3y + 12 = 0
    Gives y = -3/2, -4
    Put all values on number line and analyze the relationship
    -4……. -3/2…… 1/2….. 3
  6. I. 3x2 + 22x + 35 = 0
    II. 6y2 + 11y – 7 = 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:

    3x2 + 22x + 35 = 0
    3x2 + 15x + 7x + 35 = 0
    Gives x = -5, -7/3
    6y2 + 11y – 7 = 0
    6y2 – 3y + 14y – 7 = 0
    Gives y = 1/2, -7/3
    Put all values on number line and analyze the relationship
    -5….. -7/3….. 1/2
  7. I. 2x2 – 3x – 9 = 0
    II. 3y2 + 11y + 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:

    2x2 – 3x – 9 = 0
    2x2 – 6x + 3x – 9 = 0
    Gives x = -3/2, 3
    3y2 + 11y + 6 = 0
    3y2 + 9y + 2y + 6 = 0
    Gives y = -3, -2/3
    Put all values on number line and analyze the relationship
    -3….. -3/2….. -2/3…. 3
  8. I. x2 + 14x + 45 = 0
    II. 3y2 – y – 10 = 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:

    x2 + 14x + 45 = 0
    x2 + 9x + 5x + 45 = 0
    Gives x = -9, -5
    3y2 – y – 10 = 0
    3y2 – 6y + 5y – 10 = 0
    Gives y = -5/3, 2
    Put all values on number line and analyze the relationship
    -9…….. -5….. -5/3……. 2
  9. I. 4x2 + 17x + 15 = 0
    II. 4y2 – 3y – 10 = 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 + 17x + 15 = 0
    4x2 + 12x + 5x + 15 = 0
    Gives x = -3, -5/4
    4y2 – 3y – 10 = 0
    4y2 – 8y + 5y – 10 = 0
    Gives y = -5/4, 2
    Put all values on number line and analyze the relationship
    -3…… -5/4…… 2
  10. I. 2x2 – 17x + 36 = 0
    II. 3y2 – 14y + 8 = 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 – 17x + 36 = 0
    2x2 – 8x – 9x + 36 = 0
    Gives x = 4, 9/2
    3y2 – 14y + 8 = 0
    3y2 – 12y + 2y + 8 = 0
    Gives y = 2/3, 4
    Put all values on number line and analyze the relationship
    2/3…… 4…… 9/2

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