Quantitative Aptitude: Quadratic Equations Set 3

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 + 20x + 32 = 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 + 20x + 32 = 0
    3x2 + 12x + 8x + 32 = 0
    So x = -4, -8/3
    3y2 – 4y – 4 = 0
    3y2 – 6y + 2y – 4 = 0
    So y = -2/3, 2
    Put all values on number line and analyze the relationship
    -4… -8/3… -2/3… 2
  2. I. 4x2 – 12x + 5 = 0,
    II. 6y2 – 13y + 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:

    4x2 – 12x + 5 = 0
    4x2 – 2x – 10x + 5 = 0
    So x = ½, 5/2
    6y2 – 13y + 6 = 0
    6y2 – 4y – 9y + 6 = 0
    So y = 2/3, 3/2
    Put all values on number line and analyze the relationship
    1/2… 2/3… 3/2…. 5/2
  3. I. 32 – 14x + 16 = 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 C
    Solution:

    32 – 14x + 16 = 0
    32 – 6x – 8x + 16 = 0
    So x = 8/3, 2
    4y2 – 5y – 6 = 0
    4y2 – 8y + 3y – 6 = 0
    So y = -3/4, 2
    Put all values on number line and analyze the relationship
    -3/4 …. 2 ….8/3
  4. I. 5x2 – 8x – 4 = 0,
    II. 5y2 – 23y – 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 E
    Solution:

    5x2 – 8x – 4 = 0
    5x2 – 10x + 2x – 4 = 0
    So x = -2/5, 2
    5y2 – 23y – 10 = 0
    5y2 – 25y + 2y – 10 = 0
    So y = -2/5, 5
    Put all values on number line and analyze the relationship
    -2/5 …. 2….. 5
  5. I. 3x2 + 13x + 14 = 0,
    II. 4y2 + 9y + 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 D
    Solution:

    3x2 + 13x + 14 = 0
    3x2 + 6x + 7x + 14 = 0
    So x = -7/3, -2
    4y2 + 9y + 2 = 0
    4y2 + 8y + y + 2 = 0
    So y = -2, -1/4
    Put all values on number line and analyze the relationship
    -7/3 …. -2…. -1/4
  6. I. 3x2 + 8x + 5 = 0,
    II. 5y2 – 7y – 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 B
    Solution:

    3x2 + 8x + 5 = 0
    3x2 + 3x + 5x + 5 = 0
    So x = -5/3, -1
    5y2 – 7y – 6 = 0
    5y2 – 7y – 6 = 0
    So y = -3/5, 2
    Put all values on number line and analyze the relationship
    -5/3…. -1…. -3/5…. 2
  7. I. 3x2 ¬¬+ 16x + 20 = 0,
    II. 3y2 + 14y + 16 = 0

    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:

    3x2 ¬¬+ 16x + 20 = 0
    3x2 ¬¬+ 6x + 10x + 20 = 0
    So x = -10/3, -2
    3y2 + 14y + 16 = 0
    3y2 + 6y + 8y + 16 = 0
    So y = -8/3, -2
    Put all values on number line and analyze the relationship
    -10/3…. -8/3…. -2
  8. I. 4x2 – 9x + 2 = 0,
    II. 3y2 – 16y + 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 B
    Solution:

    4x2 – 9x + 2 = 0
    4x2 – 8x – x + 2 = 0
    So x = 1/4, 2
    3y2 – 16y + 21 = 0
    3y2 – 9y – 7y + 21 = 0
    So y = 7/3, 3
    Put all values on number line and analyze the relationship
    1/4…. 2…. 7/3… 3
  9. I. 3x2 + 5x + 2 = 0,
    II. 3y2 + 11y + 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 A
    Solution:

    3x2 + 5x + 2 = 0
    3x2 + 3x + 2x + 2 = 0
    So x = -1, -2/3
    3y2 + 11y + 10 = 0
    3y2 + 6y + 5y + 10 = 0
    So y = -2, -5/3
    Put all values on number line and analyze the relationship
    -2….. -5/3…. -1….. -2/3
  10. I. 4x2 – 9x + 2 = 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:

    4x2 – 9x + 2 = 0
    4x2 – 8x – x + 2 = 0
    So x = 1/4, 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
    1/4……. 2…… 5/2…7

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