Quantitative Aptitude: Quadratic Equations Set 10

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. 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
  3. 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
  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. 6x2 + 5x – 1 = 0,
    II. 3y2 – 11y + 6 = 0
    A) If X > Y
    B) If X < Y
    C) If X ≥ Y
    D) If X ≤ Y
    E) If X = Y or relation cannot be established
    View Answer
    Option B
    Solution:

    6x2 + 5x – 1 = 0
    6x2 + 6x – x – 1 = 0
    Gives x = -1, 1/6
    3y2 – 11y + 6 = 0
    3y2 – 9y – 2y + 6 = 0
    Gives y = 2/3, 3
    Put on number line
    -1… 1/6… 2/3… 3
  6. I. 3x2 + 4x – 4 = 0,
    II. 4y2 + 5y – 6 = 0
    A) If X > Y
    B) If X < Y
    C) If X ≥ Y
    D) If X ≤ Y
    E) If X = Y or relation cannot be established
    View Answer
    Option E
    Solution:

    3x2 + 4x – 4 = 0
    3x2 + 6x – 2x – 4 = 0
    Gives x = -2, 2/3
    4y2 + 5y – 6 = 0
    4y2 + 5y – 6 = 0
    Gives y = -2, 3/4
    Put on number line
    -2…. 2/3… 3/4
    When x=2/3, x>y(= -2) and x<y(= 3/4)
    So cant be determined
  7. I. 5x2 – 36x – 32 = 0,
    II. 3y2 – 17y – 6 = 0
    A) If X > Y
    B) If X < Y
    C) If X ≥ Y
    D) If X ≤ Y
    E) If 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
    Put on number line
    -4/5…. -1/3… 6… 8
  8. I. 3x2 – 25x + 52 = 0,
    II. 15y2 – 38y – 40 = 0
    A) If X > Y
    B) If X < Y
    C) If X ≥ Y
    D) If X ≤ Y
    E) If X = Y or relation cannot be established
    View Answer
    Option A
    Solution:

    3x2 – 25x + 52 = 0
    3x2 – 12x – 13x + 52 = 0
    Gives x = 4, 13/3
    15y2 – 38y – 40 = 0
    15y2 + 12y – 50y – 40 = 0
    Gives y = -4/5, 10/3
    Put on number line
    -4/5… 10/3… 4… 13/3
  9. I. 6x2 + x – 2 = 0,
    II. 2y2 + 11y + 14 = 0
    A) If X > Y
    B) If X < Y
    C) If X ≥ Y
    D) If X ≤ Y
    E) If X = Y or relation cannot be established
    View Answer
    Option A
    Solution:

    6x2 + x – 2 = 0
    6x2 + 4x – 3x – 2 = 0
    Gives x = -2/3, 1/2
    2y2 + 11y + 14 = 0
    2y2 + 4y + 7y + 14 = 0
    Gives y = -7/2, -2
  10. I. 3x2 + 14x – 5 = 0,
    II. 3y2 – 19y + 6 = 0
    A) If X > Y
    B) If X < Y
    C) If X ≥ Y
    D) If X ≤ Y
    E) If X = Y or relation cannot be established
    View Answer
    Option D
    Solution:

    3x2 + 14x – 5 = 0
    3x2 + 15x – x – 5 = 0
    Gives x = -5, 1/3
    3y2 – 19y + 6 = 0
    3y2 – 18y – y + 6 = 0
    Gives y = 1/3, 6
    Put on number line
    -5…. 1/3… 6

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7 Thoughts to “Quantitative Aptitude: Quadratic Equations Set 10”

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  2. Chotu D(mind) !! {NONSENSE}

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