Quantitative Aptitude: Quadratic Equations Set 4

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. 6x2 + 7x -3 = 0
    II. y (10y – 1) = 2
    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:

    6 x2 + 7x -3 = 0
    6 x2 + 9x – 2x – 3 = 0
    So x = -1.5, 0.3
    y (10y – 1) = 2
    10y2 – y – 2 = 0
    10y2 – 5y + 4y – 2 = 0
    So y = 0.5, -0.4
    Put all values on number line and analyze the relationship
    -1.5… -0.4… 0.3… 0.5
  2. I. 4x2 + 3x – 27 = 0
    II. 15y2 – 38y – 21 = 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 + 3x – 27 = 0
    4x2 + 12x – 9x – 27 = 0
    So x =2.25, -3
    15y2 – 38y – 21 = 0
    15y2 – 45y + 7y – 21 = 0
    So y = 3, – 0.46
    Put all values on number line and analyze the relationship
    -3… -0.46… 2.25…. 3
  3. I. 8x2 + 5x – 13 = 0
    II. 2y2 + 23y + 63 = 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 + 5x – 13 = 0
    8x2 + 13x – 8x – 13 = 0
    So x = -1.625, 1
    2y2 + 23y + 63 = 0
    2y2 + 14y + 9y + 63 = 0
    So y = -7, -4.5
    Put all values on number line and analyze the relationship
    -7…. -4.5 ….-1.625…. 1
  4. I. 4x2 + 19x + 21 = 0
    II. 2y2 – 25y – 27 = 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 + 19x + 21 = 0
    4x2 + 12x + 7x + 21 = 0,
    So x = -3, – 1.75
    2y2 – 25y – 27 = 0
    2y2 – 27y + 2y – 27 = 0
    So y = 13.5, -1
    Put all values on number line and analyze the relationship
    -3…. -1.75….. -1…..13.5
  5. I. x2 – 9x + 20 = 0
    II. y2 – 11y + 30 = 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:

    x2 – 9x + 20 = 0
    x2 – 4x – 5x + 20 = 0
    So x = 4, 5
    y2 – 11y + 30 = 0
    y2 – 5y -6y + 30 = 0
    So y = 5, 6
    Put all values on number line and analyze the relationship
    4 …. 5….5……6
  6. I. x2 – 7x + 12 = 0
    II. y2 – 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:

    x2 – 7x + 12 = 0
    x2 – 3x – 4x + 12 = 0
    So x = 3, 4
    y2 – 5y + 6 = 0
    y2 – 3y – 2y + 6 = 0
    So y = 2, 3
    Put all values on number line and analyze the relationship
    2…. 3….3…. 4
  7. I. x2 – 2x – 15 = 0
    II. y2 + 22 = 122
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
    Option E
    Solution:

    x2 – 2x – 15 = 0
    x2 – 5x + 3x – 15 = 0
    So x = 5, -3
    y2 + 22 = 122
    y2 = 100
    y = + 10, -10
    Put all values on number line and analyze the relationship
    -10….-3….5….10
  8. I. x2 + x – 30 = 0
    II. y2 – 11y + 30 = 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:

    x2 + x – 30 = 0
    x2 + 6x – 5x – 30 = 0
    So x = – 6, 5
    y2 – 11y + 30 = 0
    y2 – 5y – 6y + 30 = 0
    So y = 5, 6
    Put all values on number line and analyze the relationship
    -6…. 5…. 5… 6
  9. I. 2 + 5x – 14 = 0
    II. y2 + 24y + 128 = 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:

    x2 + 5x – 14 = 0
    x2 + 7x – 2x – 14 = 0
    So x = -7, 2
    y2 + 24y + 128 = 0
    y2 + 16y + 8y + 128 = 0
    So y = -16, -8
    Put all values on number line and analyze the relationship
    -16…..-8….. -7….2
  10. I. x2 – 6x – 91 = 0
    II. y2 – 32y + 247 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
    Option D
    Solution:

    x2 – 6x – 91 = 0
    x2 – 13x + 7x – 91 = 0
    So x = 13, -7
    y2 – 32y + 247 = 0
    y2 – 19y -13y + 247 = 0
    So y = 19, 13
    Put all values on number line and analyze the relationship
    -7…13…13…19

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