Quantitative Aptitude: Quadratic Equations Questions Set 45


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.(x-3)(x+2) = 0
    II. x2 – 27x + 182 = 0

    x>y
    y>x
    x>=y
    y>=x
    None of these
    Option B
    I.(x-3)(x+2) = 0
    => x= -2,3
    II.x2 – 27x + 182 = 0
    => y = 13,14
    x>y

     

  2. I. (x – 2)(x + 1) = (x – 1)(x + 3)
    II. (y + 3)(y – 2) = (y + 1)(y + 2)

    x>y
    y>=x
    x>=y
    y>x
    No relation
    Option A
    I. (x – 2)(x + 1) = (x – 1)(x + 3)
    => x = 1/3
    II. (y + 3)(y – 2) = (y + 1)(y + 2)
    => y = – 4
    x>y

     

  3. I. x2 + √3x + ¾ = 0
    II. y2 – √3y – √2y + √6 = 0

    x>y
    y>=x
    No relation
    y>x
    x>=y
    Option D
    I. x2 + √3x + ¾ = 0 => x2 + √3x + ¾ + (√3/2)2 – (√3/2)2 = 0
    => (x + √3/2)2 = 0
    => x = – √3/2 , – √3/2
    II. y2 – √3y – √2y + √6 = 0
    =>y2 – √3y – √2y + √6 = 0
    =>y (y-√3) – √2(y-√3) = 0
    =>(y-√2) (y-√3) = 0
    =>y = 1.414, 1.732
    y>x

     

  4. I. 1/(x+4) – 1/(x-7) = 11/30
    II. 1/(y-3) + 1/(y+5) = 1/3

    y>=x
    x>y
    y>=x
    No relation
    y>x
    Option D
    I. 1/(x+4) – 1/(x-7) = 11/30
    => x2 – 3x -28 = -30
    => x2 – 2x – x – 28 = -30
    => x = 1, 2
    II. 1/(y-3) + 1/(y+5) = 1/3
    =>y2 – 4y – 21 = 0
    => y = 7, -3
    No relation

     

  5. I. √2x2 + 7x + 5√2 = 0
    II. 2y2 – y + 1/8 = 0

    x>=y
    y>x
    y>=x
    No relation
    x>y
    Option B
    I. √2x2 + 7x + 5√2 = 0
    => √2x2 + 2x + 5x + 5√2 = 0
    => x = -5√2/2 , -√2
    II. 2y2 – y + 1/8 = 0
    => 16y2 – 8y + 1 = 0
    => y = 1/4 , 1/4
    y>x

     

  6. I. x(2x + 3) = 90
    II.y2 + (y + 1)2 = 365

    No relation
    y>x
    x>y
    x>=y
    y>=x
    Option A
    I.x(2x + 3) = 90
    =>x= -7.5,6
    II. y2 + (y + 1)2 = 365
    => y2 + y2 +1 + 2y = 365
    => y2 + y – 182 = 0
    => y = -14,13
    No relation

     

  7. I. √225x + √900 = 0
    II.(81)1/4y + (729)1/3=0

    y>=x
    y>x
    x>=y
    No relation
    x>y
    Option E
    I. √225x + √900 = 0
    =>15x = – 30
    => x= -2
    II.(81)1/4y + (729)1/3=0
    => 3y = -9
    => y = -3
    x >y

     

  8. I. 55x2 – 495x +1100 = 0
    II. 5y2 + 10y – 120 = 0

    y>=x
    x>=y
    No relation
    y>x
    y>x
    Option B
    I. 55x2 – 220x -275x +1100=0
    => x = 4,5
    II. 5y2 + 30y -20y – 120 =0
    => y = -6,4
    x≥y

     

  9. I. x2 – 87x – 270 = 0
    II.7y2 – 11y -18 = 0

    x>y
    No relation
    x>=y
    y>x
    y>=x
    Option B
    I. x2 -90x + 3x -270 =0
    => x = 90, -3
    II. 7y2 -18y +7y -18 = 0
    => y = 18/7, -1
    No relation

     

  10. I. 2x2 – x – 231 = 0
    II. 2y2 + 43y + 231 = 0

    x>y
    y>=x
    y>x
    x>=y
    No relation
    Option D
    I. 2x2 – 22x + 21x – 231 = 0
    => x = 11, -10.5
    II. 2y2 + 21y + 22y +231 = 0
    => y = -10.5 , -11
    x≥y

     


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