Quantitative Aptitude: Quadratic Equations Questions Set 45

Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly-

1. I.(x-3)(x+2) = 0
   II. x² – 27x + 182 = 0
   x>y
   y>x
   x>=y
   y>=x
   None of these
   Option B
   I.(x-3)(x+2) = 0
   => x= -2,3
   II.x² – 27x + 182 = 0
   => y = 13,14
   x>y

    

2. I. (x – 2)(x + 1) = (x – 1)(x + 3)
   II. (y + 3)(y – 2) = (y + 1)(y + 2)
   x>y
   y>=x
   x>=y
   y>x
   No relation
   Option A
   I. (x – 2)(x + 1) = (x – 1)(x + 3)
   => x = 1/3
   II. (y + 3)(y – 2) = (y + 1)(y + 2)
   => y = – 4
   x>y

    

3. I. x² + √3x + ¾ = 0
   II. y² – √3y – √2y + √6 = 0
   x>y
   y>=x
   No relation
   y>x
   x>=y
   Option D
   I. x² + √3x + ¾ = 0 => x2 + √3x + ¾ + (√3/2)2 – (√3/2)2 = 0
   => (x + √3/2)² = 0
   => x = – √3/2 , – √3/2
   II. y² – √3y – √2y + √6 = 0
   =>y² – √3y – √2y + √6 = 0
   =>y (y-√3) – √2(y-√3) = 0
   =>(y-√2) (y-√3) = 0
   =>y = 1.414, 1.732
   y>x

    

4. I. 1/(x+4) – 1/(x-7) = 11/30
   II. 1/(y-3) + 1/(y+5) = 1/3
   y>=x
   x>y
   y>=x
   No relation
   y>x
   Option D
   I. 1/(x+4) – 1/(x-7) = 11/30
   => x² – 3x -28 = -30
   => x² – 2x – x – 28 = -30
   => x = 1, 2
   II. 1/(y-3) + 1/(y+5) = 1/3
   =>y² – 4y – 21 = 0
   => y = 7, -3
   No relation

    

5. I. √2x² + 7x + 5√2 = 0
   II. 2y² – y + 1/8 = 0
   x>=y
   y>x
   y>=x
   No relation
   x>y
   Option B
   I. √2x² + 7x + 5√2 = 0
   => √2x² + 2x + 5x + 5√2 = 0
   => x = -5√2/2 , -√2
   II. 2y² – y + 1/8 = 0
   => 16y² – 8y + 1 = 0
   => y = 1/4 , 1/4
   y>x

    

6. I. x(2x + 3) = 90
   II.y² + (y + 1)² = 365
   No relation
   y>x
   x>y
   x>=y
   y>=x
   Option A
   I.x(2x + 3) = 90
   =>x= -7.5,6
   II. y² + (y + 1)2 = 365
   => y² + y² +1 + 2y = 365
   => y² + y – 182 = 0
   => y = -14,13
   No relation

    

7. I. √225x + √900 = 0
   II.(81)^1/4y + (729)^1/3=0
   y>=x
   y>x
   x>=y
   No relation
   x>y
   Option E
   I. √225x + √900 = 0
   =>15x = – 30
   => x= -2
   II.(81)^1/4y + (729)^1/3=0
   => 3y = -9
   => y = -3
   x >y

    

8. I. 55x² – 495x +1100 = 0
   II. 5y² + 10y – 120 = 0
   y>=x
   x>=y
   No relation
   y>x
   y>x
   Option B
   I. 55x² – 220x -275x +1100=0
   => x = 4,5
   II. 5y² + 30y -20y – 120 =0
   => y = -6,4
   x≥y

    

9. I. x² – 87x – 270 = 0
   II.7y² – 11y -18 = 0
   x>y
   No relation
   x>=y
   y>x
   y>=x
   Option B
   I. x² -90x + 3x -270 =0
   => x = 90, -3
   II. 7y² -18y +7y -18 = 0
   => y = 18/7, -1
   No relation

    

10. I. 2x² – x – 231 = 0
    II. 2y² + 43y + 231 = 0
    x>y
    y>=x
    y>x
    x>=y
    No relation
    Option D
    I. 2x² – 22x + 21x – 231 = 0
    => x = 11, -10.5
    II. 2y² + 21y + 22y +231 = 0
    => y = -10.5 , -11
    x≥y