Quantitative Aptitude: Quadratic Equations Set 11

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 – 8x + 4 = 0
    II. 3y2 – 16y + 16 = 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 – 8x + 4 = 0
    3x2 – 2x – 6x + 4 = 0
    Gives x = 2, 2/3
    3y2 – 16y + 16 = 0
    3y2 – 12y – 4y + 16 = 0
    Gives y = 4, 4/3
  2. I. 3x2 + 10x + 7 = 0
    II. 2y2 – 5y – 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 + 10x + 7 = 0
    3x2 + 3x + 7x + 7 = 0
    Gives x = -1, -7/3
    2y2 – 5y – 12 = 0
    2y2 – 8y + 3y – 12 = 0
    Gives y = -3/2, 4
  3. I. 4x2 + 15x + 9 = 0
    II. 4y2 – 13y – 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 D
    Solution:

    4x2 + 15x + 9 = 0
    4x2 + 12x + 3x + 9 = 0
    Gives x = -3, -3/4
    4y2 – 13y – 12 = 0
    4y2 – 16y + 3y – 12 = 0
    Gives y = -3/4, 4
  4. I. 3x2 + 23x + 30 = 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 B
    Solution:

    3x2 + 23x + 30 = 0
    3x2 + 18x + 5x + 30 = 0
    Gives x = -5/3, -6
    3y2 – 4y – 4 = 0
    3y2 – 6y + 2y – 4 = 0
    Gives y = 2, -2/3
    Put all values on number line and analyze the relationship
    -6…. -5/3….. -2/3…… 2
  5. I. 5x2 – 36x – 32 = 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:

    5x2 – 36x – 32 = 0
    5x2 + 4x – 40x – 32 = 0
    Gives x = -4/5, 8
    3y2 – 17y – 6 = 0
    3y2 + y – 18y – 6 = 0
    Gives y = -1/3, 6
  6. I. 4x2 + 17x + 18 = 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 D
  7. I. 4x2 – 9x – 9 = 0,
    II. 4y2 + 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 C
  8. I. 3x2 – 19x + 28 = 0,
    II. 4y2 – 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 A
  9. I. 3x2 + 19x + 28 = 0,
    II. 6y2 – y – 2 = 0A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option B

  10. I. 3x2 + 7x – 6 = 0,
    II. 6y2 – y – 2 = 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 + 7x – 6 = 0
    3x2 + 9x – 2x – 6 = 0
    Gives x = -3, 2/3
    6y2 – y – 2 = 0
    6y2 + 3y – 4y – 2 = 0
    Gives y = -1/2, 2/3

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