Quantitative Aptitude: Quadratic Equations Questions Set 59

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

1. I.x^2 +36x + 323 = 0
   II.y^2 + 30y +221 = 0
   
   x > y
   y > x
   x >= y
   No relation.
   y >= x
   Option E
   I.x^2 +36x + 323 = 0
   => x^2 +17x + 19x +323 = 0
   =>x = -17,-19
   II.y^2 + 30y +221 = 0
   =>y^2 + 13y + 17y + 221 = 0
   =>y = -13,-17
   y >= x
   
   
    



2. I.x^2 +2x – 24 = 0
   II.y^2 + 2y – 15 = 0
   
   x >= y
   x > y
   y >= x
   y > x
   No relation.
   Option E
   I.x^2 +2x – 24 = 0
   =>x^2 + 6x – 4x – 24 = 0
   =>x = -6,4
   II.y^2 + 2y – 15 = 0
   =>y^2 + 5y – 3y – 15 = 0
   =>y = -5,3
   No relation.
   
   
    



3. I.x^2 – 29x + 180 = 0
   II.y^2 + 10y – 171 = 0
   
   x > y
   y > x
   No relation.
   y >= x
   x >= y
   Option E
   I.x^2 – 29x + 180 = 0
   =>x^2 – 20x – 9x + 180 = 0
   =>x = 20,9
   II.y^2 + 10y – 171 = 0
   =>y^2 + 19y – 9y – 171 = 0
   =>(y+19)(y - 9) = 0
   =>y = -19,9
   x >= y
   
   
    



4. I.x^2 +15x + 50 = 0
   II.y^2 + 23y + 132 = 0
   
   y >= x
   x >= y
   y > x
   x > y
   No relation.
   Option D
   I.x^2 +15x + 50 = 0
   =>x^2 + 5x + 10x + 50 = 0
   =>x = -5,-10
   II.y^2 + 23y + 132 = 0
   =>y^2 + 11y + 12y + 132 = 0
   =>y = -11,-12
   x > y
   
   
    



5. I.x^2 + 29x + 210 = 0
   II.y^2 + 34y + 288 = 0
   
   x >= y
   y >= x
   x > y
   y > x
   No relation.
   Option C
   I.x^2 + 29x + 210 = 0
   =>x^2 + 15x + 14x + 210 = 0
   =>x = -15,-14
   II.y^2 + 34y + 288 = 0
   =>y^2 + 16y +18y + 288 = 0
   =>y = -16,-18
   x > y
   
   
    



6. I.7x^2 +44x – 35 = 0
   II.4y^2 - 33y + 35 = 0
   
   y > x
   x >= y
   x > y
   No relation.
   y >= x
   Option A
   I.7x^2 +44x – 35 = 0
   =>7x^2 – 5x + 49x – 35 = 0
   =>x = -7,5/7
   II.4y^2 - 33y + 35 = 0
   =>4y^2 – 5y – 28y + 35 = 0
   =>y = 7,5/4
   y > x
   
   
   
    



7. I.x^2 + 8x – 128 = 0
   II.y^2 - 17y + 72 = 0
   
   x >= y
   No relation.
   y > x
   y >= x
   x > y
   Option D
   I.x^2 + 8x – 128 = 0
   =>x^2 + 16x – 8x – 128 = 0
   =>x = 8,-16
   II.y^2 - 17y + 72 = 0
   =>y^2 – 9y – 8y + 72 = 0
   =>y = 9,8
   y >= x
   
   
    



8. I.x^2 + 5x – 204 = 0
   II.y^2 + y – 156 = 0
   
   x >= y
   No relation.
   y >= x
   x > y
   y > x
   Option B
   I.x^2 + 5x – 204 = 0
   =>x^2 + 17x – 12x – 204 = 0
   =>x = -17,12
   II.y^2 + y – 156 = 0
   =>y^2 + 13y – 12y – 156 = 0
   =>y = -13,12
   No relation.
   
   
    



9. I.x^2 – 28x + 195 = 0
   II.y^2 – 36x + 323 = 0
   
   y >= x
   x > y
   y > x
   No relation.
   x >= y
   Option C
   I.x^2 – 28x + 195 = 0
   =>x^2 – 15x – 13x + 195 = 0
   =>x = 15,13
   II.y^2 – 36x + 323 = 0
   =>y^2 – 17y – 19y + 323 = 0
   =>y = 17,19
   y > x
   
   
    



10. I.x^2 - 10x + 24 = 0
    II.y^2 – 18y + 77 = 0
    
    No relation.
    x > y
    y >= x
    x >= y
    y > x
    Option E
    I.x^2 - 10x + 24 = 0
    =>x^2 – 4x – 6x + 24 = 0
    =>x = 4,6
    II.y^2 – 18y + 77 = 0
    =>y^2 – 11y – 7y + 77 = 0
    =>y = 11,7
    y > x