Quantitative Aptitude: Quadratic Equations Questions Set 52

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

1. I.x^2 – 13x + 42 = 0
   II.y^2 – 14y + 45 = 0
   x>y
   y>=x
   No relation
   x>=y
   y>x
   Option C
   I.x^2 – 13x + 42 = 0
   =>x^2 – 7x – 6x + 42 = 0
   => (x-7)(x-6) = 0
   => x = 7,6
   II.y^2 – 14y + 45 = 0
   =>y^2 -9y – 5y + 45 = 0
   => (y-9)(y-5) = 0
   => y = 9,5
   No relation.

    

2. I.6x^2 – 31x + 18 = 0
   II.2y^2 – 22y + 60 = 0
   y>=x
   x>y
   y>x
   x>=y
   No relation
   Option C
   I.6x^2 – 31x + 18 = 0
   => 6x^2 – 27x – 4x + 18 = 0
   => (2x – 9)(3x-2)= 0
   => x = 4.5,0.66
   II.2y^2 – 22y + 60 = 0
   =>2y^2 -12y – 10y + 60 = 0
   =>(y-6)(2y-10)= 0
   =>y = 6,5
   y>x

    

3. I.5x^2 – 27x + 10 = 0
   II.y^2 – 18y + 72 = 0
   x>y
   No relation
   y>x
   y>=x
   x>=y
   Option C
   I.5x^2 – 27x + 10 = 0
   => 5x^2 – 25x – 2x + 10 = 0
   => (x-5)(5x-2) = 0
   => x = 5,2/5
   II.y^2 – 18y + 72 = 0
   =>y^2 – 12y -6y + 72 = 0
   => (y-12)(y-6) = 0
   =>y = 12,6
   y>x

    

4. I.x^2 + 15x + 56 = 0
   II.y^2 + 11y + 30 = 0
   No relation
   x>=y
   y>=x
   x>y
   y>x
   Option E
   I.x^2 + 15x + 56 = 0
   => x^2 + 7x + 8x + 56 = 0
   => (x+8)(x+7) = 0
   => x = -8,-7
   II.y^2 + 11y + 30 = 0
   =>y^2 + 5y + 6y + 30 = 0
   => (y+6)(y+5) = 0
   => y = -6,-5
   y>x

    

5. I.x^2 + 31x +234 = 0
   II.y^2 – 2y – 195 = 0
   x>=y
   y>x
   No relation
   x>y
   y>=x
   Option E
   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 = -13,15
   y>=x

    

6. I.4x+9y = 77
   II.11x -4y = 68
   x>=y
   y>x
   y>=x
   No relation
   x>y
   Option E
   On solving both the equations,we get
   x = 8
   y = 5
   x>y

    

7. I.x^2 -15x + 54 = 0
   II.3y^2-25y+ 42 = 0
   x>y
   x>=y
   y>x
   No relation
   x>=y
   Option E
   I.x^2 -15x + 54 = 0
   =>x^2 – 9x – 6x + 54 =0
   => (x-9)(x-6) = 0
   => x= 9,6
   II.3y^2-25y+ 42 = 0
   =>3y^2 – 18y -7y + 42 = 0
   =>(y-6)(3y-7)= 0
   => y = 6,7/6
   x>=y

    

8. I.x^2 +7(2)^1/2x+24 = 0
   II.y^2 +[6+4(2)^1/2]y + 24(2)^1/2 = 0
   x>=y
   No relation
   y>=x
   x>y
   y>x
   Option A
   I.x^2 +7(2)^1/2x+24 = 0
   =>x^2 + 4(2)^1/2x + 3(2)^1/2x + 24 = 0
   =>[x+4(2)^1/2][x+3(2)^1/2] = 0
   =>x = -4(2)^1/2,-3(2)^1/2
   II.y^2 +[6+4(2)^1/2]y + 24(2)^1/2 = 0
   =>y^2 + 6y +4(2)^1/2y + 24(2)^1/2 = 0
   =>(y+6)[y+4(2)^1/2] = 0
   =>y = -6,-4(2)^1/2
   x>=y

    

9. I.8x + 15y = 46
   II.7x – 2y = 10
   No relation
   x>=y
   x>y
   y>=x
   y>x
   Option A
   On solving both the equations, we get
   x = y
   No relation

    

10. I.x^2 – 20x + 96 = 0
    II.y^2 – 13y + 40 = 0
    y>=x
    y>x
    No relation
    x>y
    x>=y
    Option E
    I.x^2 – 20x + 96 = 0
    =>x^2 – 12x – 8x + 96 = 0
    => (x-8)(x-12) = 0
    => x = 8,12
    II.y^2 – 13y + 40 = 0
    =>y^2 – 8x – 5y + 40 = 0
    =>(y-8)(y-5) = 0
    => y = 8,5
    x>=y