Quantitative Aptitude: Quadratic Equations Set 2

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. 4x2 + 27x + 18 = 0,
    II. 2y2 – 7y + 3 = 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:

    4x2 + 27x + 18 = 0
    4x2 + 24x + 3x + 18 = 0
    So x = -3/4, -6
    2y2 – 7y + 3 = 0
    2y2 – 6y – y + 3 = 0
    So y = 1/2, 3
    Put all values on number line and analyze the relationship
    -6… -3/4… 1/2… 3
  2. I. 3x2 – 2x – 8 = 0,
    II. 6y2 – 17y + 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:

    3x2 – 2x – 8 = 0
    3x2 – 6x + 4x – 8 = 0
    So x = -4/3, 2
    6y2 – 17y + 10 = 0
    6y2 – 12y – 5y + 10 = 0
    So y = 5/6, 2
    Put all values on number line and analyze the relationship
    -4/3… 2… 5/6
  3. I. 32 + 11x + 6 = 0,
    II. 5y2 + 16y + 3 = 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:

    32 + 11x + 6 = 0
    32 + 9x + 2x + 6 = 0
    So x = -3, -2/3
    5y2 + 16y + 3 = 0
    5y2 + 15y + y + 3 = 0
    So y = -1/5, -3
    Put all values on number line and analyze the relationship
    -3 …. -2/3 ….-1/5
    Since the common value (-3) is not in between other 2 values, there is no relationship between x and y.
  4. I. 4x2 – 11x + 6 = 0,
    II. 6y2 – 29y + 28 = 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 – 11x + 6 = 0
    4x2 – 8x – 3x + 6 = 0
    So x = 3/4, 2
    6y2 – 29y + 28 = 0
    6y2 – 8y – 21y + 28 = 0
    So y = 4/3, 7/2
    Put all values on number line and analyze the relationship
    3/4 …. 4/3….. 2…. 7/2
  5. I. 3x2 – 25x + 52 = 0,
    II. 3y2 – 8y – 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 C
    Solution:

    3x2 – 25x + 52 = 0
    3x2 – 12x – 13x + 52 = 0
    So x = 4, 13/3
    3y2 – 8y – 16 = 0
    3y2 – 12y + 4y – 16 = 0
    So y = 4, -4/3
    Put all values on number line and analyze the relationship
    -4/3 …. 4…. 13/3
  6. I. 8x2 + 10x + 3 = 0,
    II. 3y2 + 70y + 40 = 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:

    8x2 + 10x + 3 = 0
    8x2 + 4x + 6x + 3 = 0
    So x = -3/4, -1/2
    3y2 + 70y + 40 = 0
    3y2 + 30y + 40y + 40 = 0
    So y = -10, -4/3
    Put all values on number line and analyze the relationship
    -10 … -4/3 …. -3/4 …. -1/2
  7. I. 50x2 ¬¬– 95x + 42 = 0,
    II. 50y2 – 65y + 21 = 0

    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
    Option C
    Solution:

    50x2 ¬¬– 95x + 42 = 0
    50x2 ¬¬– 60x – 35x + 42 = 0
    So x = 7/10, 6/5
    50y2 – 65y + 21 = 0
    50y2 – 65y + 21 = 0
    So y = 3/5, 7/10
    Put all values on number line and analyze the relationship
    3/5…. 7/10…. 6/5
  8. I. 5x2 – 13x + 6 = 0,
    II. 3y2 – 22y – 35 = 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:

    5x2 – 13x + 6 = 0
    5x2 – 10x – 3x + 6 = 0
    So x = 3/5, 2
    3y2 – 22y – 35 = 0
    3y2 – 15y – 7y – 35 = 0
    So y = 7/3, 5
    Put all values on number line and analyze the relationship
    3/5…. 2…. 7/3… 5
  9. I. 3x2 – 4x – 15 = 0,
    II. 5y2 – 11y – 18 = 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 – 15 = 0
    3x2 – 9x + 5x – 15 = 0
    So x = -5/3, 3
    5y2 – 11y – 18 = 0
    5y2 – 15y + 6y – 18 = 0
    So y = -6/5, 3
    Put all values on number line and analyze the relationship
    -5/3….. -6/5…. 3
    Since the common value (3) is not in between other 2 values, there is no relationship between x and y.
  10. I. 2x2 + 5x – 12 = 0,
    II. 2y2 – 19y + 35 = 0

    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
    Option B
    Solution:

    2x2 + 5x ¬– 12 = 0
    2x2 + 8x ¬– 3x – 12 = 0
    So x = -4 , 3/2
    2y2 – 19y + 35 = 0
    2y2 – 14y – 5y + 35 = 0
    So y = 5/2, 7
    Put all values on number line and analyze the relationship
    -4……. 3/2…… 5/2…

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