# 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