Quantitative Aptitude: Quadratic Equations Questions Set 61

Directions(1-10): Find the values of x and y, compare and choose a correct option.

  1. I.x^2 – 9x + 20 = 0
    II.y^2 – 7y + 12 = 0
    y > x
    x > y
    No relation
    x >= y
    y >= x
    Option D
    I.x^2 – 9x + 20 = 0
    =>x^2 – 5x – 4x +20 = 0
    =>(x-4)(x-5) = 0
    =>x = 4,5
    II.y^2 – 7y + 12 = 0
    =>y^2 – 4y – 3y + 12 =0
    =>(y-3)(y-4) = 0
    =>y = 4,3
    x >= y

     

  2. I.x^2 – 16x +63 = 0
    II.y^2 + 11y + 24 = 0
    y > x
    y >= x
    x > y
    No relation
    x >= y
    Option C
    I.x^2 – 16x +63 = 0
    =>x^2 -9x -7x+63 =0
    =>(x-9)(x-7) = 0
    =>x= 7,9
    II.y^2 + 11y + 24 = 0
    =>y^2 +8y +3y + 24= 0
    =>(y+8)(y+3) = 0
    =>y = -3,-8
    x > y

     

  3. I.4x + 3y = 21
    II.5x – 2y = 9
    x >= y
    No relation
    y >= x
    x > y
    y > x
    Option B
    On solving both the equations, we get
    x =y = 3
    No relation

     

  4. I.x^2 +33x + 272 = 0
    II.y^2 + y – 306 = 0
    y >= x
    No relation
    x >= y
    x > y
    y > x
    Option B
    I.x^2 +33x + 272 = 0
    =>x^2 + 17x + 16x + 272 = 0
    =>(x+17)(x+16) =0
    =>x = -17,-16
    II.y^2 + y – 306 = 0
    =>y^2 + 18y – 17y -306= 0
    =>(y+18)(y-17) = 0
    =>y = -18,17
    No relation

     

  5. I.2x^2 = 11x – 15
    II.2y^2 = y + 10
    y > x
    x >= y
    y >= x
    No relation
    x > y
    Option B
    I.2x^2 = 11x – 15
    =>2x^2 – 6x – 5x + 15= 0
    =>(2x -5)(x -3) = 0
    =>x = 3,5/2
    II.2y^2 = y + 10
    =>2y^2 -5y +4y -10 =0
    =>(y+2)(2y-5) = 0
    =>y = -2,5/2
    x >= y

     

  6. I.x^2 – 16 = 0
    II.y = (16)^1/2
    y > x
    x > y
    y >= x
    x >= y
    No relation
    Option C
    I.x^2 – 16 = 0
    => x = -4,+4
    II.y = (16)^1/2
    => y = 4
    y >= x

     

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

     

  8. I.x + y = 9
    II.2x – y = 6
    y >= x
    x >= y
    y > x
    x > y
    No relation
    Option D
    On solving both the equations, we get
    x = 5
    y = 4
    x > y

     

  9. I.x^2 + 13x +36 = 0
    II.y^2 + 15y + 56 = 0
    y > x
    x >= y
    x > y
    No relation
    y >= x
    Option D
    I.x^2 + 13x +36 = 0
    => x^2 + 9x + 4x + 36 = 0
    =>(x+9)(x+4) = 0
    =>x = -9,-4
    II.y^2 + 15y + 56 = 0
    =>y^2 + 8y + 7y + 56 = 0
    =>(y+8)(y+7) = 0
    => y = -8,-7
    No relation

     

  10. I.x^2 +5x +6 =0
    II.y^2 + 2y – 8 = 0
    y >= x
    y > x
    x >= y
    x > y
    No relation
    Option E
    I.x^2 +5x +6 =0
    =>x^2 + 2x + 3x + 6 = 0
    =>(x+2)(x+3) = 0
    =>x = -2,-3
    II.y^2 + 2y – 8 = 0
    =>y^2 + 4y – 2y – 8 = 0
    =>(y+4)(y-2)=0
    =>y = -4,2
    No relation

     


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