Quantitative Aptitude: Quadratic Equations Questions Set 53

Directions(1-10): Comparing I and II and select a required option.

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

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

     

  2. I.4x^2 – 20x + 21 = 0
    II.4y^2 = 4y + 15

    x>=y
    No relation.
    y>x
    x>y
    y>=x
    Option B
    I.4x^2 – 20x + 21 = 0
    =>4x^2 – 14x – 6x + 21 = 0
    =>(2x- 7)(2x – 3) = 0
    => x = 3/2,7/2
    II.4y^2 = 4y + 15
    =>4y^2 – 10y + 6y – 15 =0
    =>(2y – 15)(2y+3) = 0
    =>y = -3/2,5/2
    No relation.

     

  3. I.3x^2 +14x +15 = 0
    II.2y^2 = 3y + 5

    y>=x
    x>=y
    x>y
    No relation.
    y>x
    Option E
    I.3x^2 +14x +15 = 0
    =>3x^2 + 9x + 5x + 15 = 0
    =>3x(x+3)+5(x+3) = 0
    =>(3x+5)(x+3) =0
    =>x = -5/3,-3
    II.2y^2 = 3y + 5
    =>2y^2 – 5y + 2y – 5 = 0
    =>(y+1)(2y-5) = 0
    =>y = -1,5/2
    y>x

     

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

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

     

  5. I.5x + 9y = 112
    II.9x – 2y = 56

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

     

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

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

     

  7. I.x^2 + 31x + 234 = 0
    II.y^2 – 2y – 195 = 0

    y>=x
    y>x
    x>y
    x>=y
    No relation.
    Option A
    I.x^2 + 31x + 234 = 0
    =>x^2 + 18x + 13x + 234 = 0
    =>(x+18)(x+13) = 0
    => x = -18,-13
    II.y^2 – 2y – 195 = 0
    =>y^2 – 15y + 13y – 195 = 0
    =>(y-15)(y+13) = 0
    =>y = 15,-13
    y>=x

     

  8. I.x + 20(x)^1/2 + 96 = 0
    II.y – 4(y)^1/2 – 140 = 0

    No relation.
    y>x
    y>=x
    x>y
    x>=y
    Option A
    I.x + 20(x)^1/2 + 96 = 0
    =>(x^2)^1/2 + 20(x)^1/2 + 96 = 0
    =>(x^2)^1/2 + 12(x)^1/2 + 8(x)^1/2 + 96 = 0
    =>[(x)^1/2 + 12][(x)^1/2 + 8] = 0
    =>x = 144,64
    II.y – 4(y)^1/2 – 140 = 0
    =>(y^2)^1/2 – 4(y)^1/2 – 140 = 0
    =>(y^2)^1/2 – 14(y)^1/2 + 10(y)^1/2 – 140 = 0
    =>[(y)^1/2 – 14][(y)^1/2 + 10] = 0
    => y = 100,196
    No relation.

     

  9. I.x^2 + 9(3)^1/2x + 54 = 0
    II.y^2 + [11 + 7(3)^1/2]y + 77(3)^1/2 = 0

    x>=y
    No relation.
    y>x
    y>=x
    x>y
    Option E
    I.x^2 + 9(3)^1/2x + 54 = 0
    =>x^2 + 6(3)^1/2x + 3(3)^1/2x + 54 = 0
    =>[x+6(3)^1/2][x+3(3)^1/2] = 0
    =>x = -6(3)^1/2,-3(3)^1/2
    II.y^2 + [11 + 7(3)^1/2]y + 77(3)^1/2 = 0
    =>y^2 + 11y + 7(3)^1/2y + 77(3)^1/2 = 0
    =>(y+11)[y+7(3)^1/2] = 0
    =>y = -11,-7(3)^1/2
    x>y

     

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

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

     


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