Quantitative Aptitude: Quadratic Equations Set 9

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. 8/√x + 9/(√x +1) = 7,
    II. 9/√y – 3/√y = 2
    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:

    8/√x + 9/(√x +1) = 7
    [8(√x +1) + 9√x]/[√x * (√x +1)] = 7
    17√x + 8 = 7 (x + √x)
    7x – 10√x – 8 = 0
    7x – 14√x + 4√x – 8 = 0
    7√x (√x – 2) + 4 (√x – 2) = 0
    √x cannot be -4/7
    So √x = 2, so x = 4
    9/√y – 3/√y = 2
    (9 – 3)/√y = 2
    Gives √y = 3, so y = 9
  2. I. 9/√x + 3/√x = √x + 1,
    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 A
    Solution:

    9/√x + 3/√x = √x + 1
    12/√x = √x + 1
    x + √x – 12 = 0
    x + 4√x – 3√x – 12 = 0
    √x(√x + 4) – 3 (√x + 4) = 0
    √x cannot be -4, So √x = 3 => x = 9
    4y2 + 5y – 6 = 0
    4y2 + 5y – 6 = 0
    Gives y = -2, 3/4
    Put all values on number line and analyze the relationship
    -2… 3/4… 9
  3. I. 6x2 + 13x + 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 B
    Solution:

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

    3x2 + 14x – 5 = 0
    3x2 + 15x – x – 5 = 0
    Gives x = -5, 1/3
    3y2 – 11y + 6 = 0
    3y2 – 9y – 2y + 6 = 0
    Gives y = 2/3, 3
    Put all values on number line and analyze the relationship
    -5… 1/3… 2/3… 3
  5. I. 6x2 + 5x – 1 = 0,
    II. 3y2 – 10y + 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:

    6x2 + 5x – 1 = 0
    6x2 + 6x – x – 1 = 0
    Gives x = -1, 1/6
    3y2 – 10y + 3 = 0
    3y2 – 9y – y + 3 = 0
    Gives y = 1/3, 3
    Put all values on number line and analyze the relationship
    -1… 1/6… 1/3… 3
  6. I. 12x2 – 5x – 3 = 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:

    12x2 – 5x – 3 = 0
    12x2 + 4x – 9x – 3 = 0
    Gives x = -1/3, 3/4
    3y2 – 11y + 6 = 0
    3y2 – 9y – 2y + 6 = 0
    Gives y = 2/3, 3
    Put all values on number line and analyze the relationship
    -1/3… 2/3… 3/4… 3
  7. I. 6x2 + 7x + 2 = 0,
    II. 15y2 – 38y – 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 E
    Solution:

    6x2 + 7x + 2 = 0
    6x2 + 4x + 3x + 2 = 0
    Gives x = -2/3, -1/2
    15y2 – 38y – 40 = 0
    15y2 + 12y – 50y – 40 = 0
    Gives y = -4/5, 10/3
    Put all values on number line and analyze the relationship
    -4/5… -2/3… -1/2… 10/3
  8. I. 3x2 – 25x + 52 = 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 A
    Solution:

    3x2 – 25x + 52 = 0
    3x2 – 12x – 13x + 52 = 0
    Gives x = 4, 13/3
    2y2 – 7y + 3 = 0
    2y2 – 6y – y + 3 = 0
    So y = 1/2, 3
    Put all values on number line and analyze the relationship
    1/2… 3… 4… 13/3
  9. I. x2 = 1156,
    II. y = √1156
    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 = 1156,
    So x = -34, 34
    y = √1156
    So y = 34
    Put all values on number line and analyze the relationship
    -34… 34
  10. I. x2 – √3969 = √6561,
    II. y2 – √1296 = √4096
    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:

    x2 – √3969 = √6561
    x2 – 63 = 81
    x2 = 144
    So x = -12, 12
    y2 – √1296 = √4096
    y2 – 36 = 64
    y2 = 100
    So y = -10, 10
    Put all values on number line and analyze the relationship
    -12… -10….10…. 12

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