Quantitative Aptitude: Quadratic Equations Questions Set 54

Directions(1-10): Comparing x and y and select a required option.

  1. I.8x^2 – 46x +63 = 0
    II.2y^2 – 17y + 35 = 0

    x>=y
    x > y
    y >= x
    y > x
    No relation.
    Option C
    From I: I.8x^2 – 46x +63 = 0
    =>8x^2 – 28x – 18x + 63 = 0
    =>(2x-7)(4x-9) = 0
    =>x = 7/2,9/4
    From II:
    II.2y^2 – 17y + 35 = 0
    =>2y^2 – 10y – 7y + 35 = 0
    =>(2y-7)(y-5) = 0
    =>y = 7/2,5
    y >= x

     

  2. I.x^2 + 11x + 28 = 0
    II.y^2 + 17y + 72 = 0

    y > x
    y >= x
    No relation.
    x > y
    x>=y
    Option D
    From I: I.x^2 + 11x + 28 = 0
    =>x2 + 4x + 7x + 28 = 0
    =>(x+7)(x+4) = 0
    => x = -7,-4
    From II: II.y^2 + 17y + 72 = 0
    =>y^2 + 9y + 8y + 72 = 0
    =>(y+9)(y+8) = 0
    => y = -9,-8
    x > y

     

  3. I.x^2 – 5x + 6 = 0
    II.y^2 + 2y – 63 = 0

    y >= x
    x > y
    y > x
    No relation.
    x>=y
    Option D
    From I:
    I.x^2 – 5x + 6 = 0
    =>x^2 – 3x – 2x + 6 = 0
    =>(x-3)(x-2) = 0
    => x= 3,2
    From II:
    II.y^2 + 2y – 63 = 0
    =>y^2 + 9y – 7y – 63 = 0
    =>(y+9)(y-7)= 0
    => y = -9,7
    No relation.

     

  4. I.12x^2 – 31x + 20 = 0
    II.10y^2 – 11y + 3 = 0

    y > x
    No relation.
    x>=y
    y >= x
    x > y
    Option E
    From I:
    I.12x^2 – 31x + 20 = 0
    =>12x^2 – 16x – 15x + 20 = 0
    =>(3x – 4)(4x – 5) = 0
    => x = 4/3,5/4
    From II:
    II.10y^2 – 11y + 3 = 0
    =>10y^2 – 5y – 6y + 3 = 0
    =>(5y-3)(2y-1) = 0
    =>y = 3/5,1/2
    x>y

     

  5. I.x^2 – 3x – 54 = 0
    II.y^2 – 19y + 90 = 0

    x > y
    No relation.
    x>=y
    y > x
    y >= x
    Option E
    From I:
    I.x^2 – 3x – 54 = 0
    =>x^2 – 9x + 6x – 54 = 0
    =>(x-9)(x+6) = 0
    =>x = 9, -6
    From II:
    II.y^2 – 19y + 90 = 0
    =>y^2 – 9y – 10y + 90 = 0
    =>(y-9)(y-10) = 0
    =>y = 9,10
    y>=x

     

  6. I.7x+3y = 40
    II.5x+6y = 44

    No relation.
    x > y
    y >= x
    y > x
    x>=y
    Option A
    On solving both the equations, we get
    x = y = 4
    No relation.

     

  7. I.x^2 – 15x + 56 = 0
    II.y^2 + 2y – 63 = 0

    y > x
    x>=y
    y >= x
    No relation.
    x > y
    Option B
    From I:
    I.x^2 – 15x + 56 = 0
    =>x^2 – 7x – 8x + 56 = 0
    =>(x-7)(x-8) = 0
    =>x = 7,8
    From II:
    II.y^2 + 2y – 63 = 0
    =>y^2 + 9y – 7y – 63 = 0
    =>(y+9)(y-7)= 0
    => y = -9,7
    x >= y

     

  8. I.7x + 8y = 80
    II.9x – 5y = 57

    x>=y
    y >= x
    x > y
    No relation.
    y > x
    Option C
    On solving both the equations,we get
    x = 8 y = 3
    x>y

     

  9. I.x^2 – 3x – 18 = 0
    II.y^2 + 8y + 15 = 0

    y >= x
    x>=y
    x > y
    y > x
    No relation.
    Option B
    From I:
    I.x^2 – 3x – 18 = 0
    =>x^2 + 3x – 6x – 18 = 0
    =>(x+3)(x-6) = 0
    =>x = -3,6
    From II:
    II.y^2 + 8y + 15 = 0
    =>y^2 + 5y + 3y + 15 = 0
    =>(y+3)(y+5)= 0
    =>y = -3,-5
    x>=y

     

  10. I.x^2 – 2x – 15 = 0
    II.y^2 + 4y – 12 = 0

    x > y
    No relation.
    y > x
    y >= x
    x>=y
    Option B
    From I:
    I.x^2 – 2x – 15 = 0
    =>x^2 – 5x + 3x – 15 = 0
    =>(x-5)(x+3)=0
    =>x = 5,-3
    From II:
    II.y^2 + 4y – 12 = 0
    =>y^2 + 6y – 2y – 12 = 0
    =>(y+6)(y-2)= 0
    =>y = -6,2
    No relation.

     


Related posts

Leave a Comment