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