# Quantitative Aptitude: Quadratic Equations Questions Set 54

Directions(1-10): Comparing x and y and select a required option.

1. I.8x^2 – 46x +63 = 0
II.2y^2 – 17y + 35 = 0

x>=y
x > y
y >= x
y > x
No relation.
Option C
From I: I.8x^2 – 46x +63 = 0
=>8x^2 – 28x – 18x + 63 = 0
=>(2x-7)(4x-9) = 0
=>x = 7/2,9/4
From II:
II.2y^2 – 17y + 35 = 0
=>2y^2 – 10y – 7y + 35 = 0
=>(2y-7)(y-5) = 0
=>y = 7/2,5
y >= x

2. I.x^2 + 11x + 28 = 0
II.y^2 + 17y + 72 = 0

y > x
y >= x
No relation.
x > y
x>=y
Option D
From I: I.x^2 + 11x + 28 = 0
=>x2 + 4x + 7x + 28 = 0
=>(x+7)(x+4) = 0
=> x = -7,-4
From II: II.y^2 + 17y + 72 = 0
=>y^2 + 9y + 8y + 72 = 0
=>(y+9)(y+8) = 0
=> y = -9,-8
x > y

3. I.x^2 – 5x + 6 = 0
II.y^2 + 2y – 63 = 0

y >= x
x > y
y > x
No relation.
x>=y
Option D
From I:
I.x^2 – 5x + 6 = 0
=>x^2 – 3x – 2x + 6 = 0
=>(x-3)(x-2) = 0
=> x= 3,2
From II:
II.y^2 + 2y – 63 = 0
=>y^2 + 9y – 7y – 63 = 0
=>(y+9)(y-7)= 0
=> y = -9,7
No relation.

4. I.12x^2 – 31x + 20 = 0
II.10y^2 – 11y + 3 = 0

y > x
No relation.
x>=y
y >= x
x > y
Option E
From I:
I.12x^2 – 31x + 20 = 0
=>12x^2 – 16x – 15x + 20 = 0
=>(3x – 4)(4x – 5) = 0
=> x = 4/3,5/4
From II:
II.10y^2 – 11y + 3 = 0
=>10y^2 – 5y – 6y + 3 = 0
=>(5y-3)(2y-1) = 0
=>y = 3/5,1/2
x>y

5. I.x^2 – 3x – 54 = 0
II.y^2 – 19y + 90 = 0

x > y
No relation.
x>=y
y > x
y >= x
Option E
From I:
I.x^2 – 3x – 54 = 0
=>x^2 – 9x + 6x – 54 = 0
=>(x-9)(x+6) = 0
=>x = 9, -6
From II:
II.y^2 – 19y + 90 = 0
=>y^2 – 9y – 10y + 90 = 0
=>(y-9)(y-10) = 0
=>y = 9,10
y>=x

6. I.7x+3y = 40
II.5x+6y = 44

No relation.
x > y
y >= x
y > x
x>=y
Option A
On solving both the equations, we get
x = y = 4
No relation.

7. I.x^2 – 15x + 56 = 0
II.y^2 + 2y – 63 = 0

y > x
x>=y
y >= x
No relation.
x > y
Option B
From I:
I.x^2 – 15x + 56 = 0
=>x^2 – 7x – 8x + 56 = 0
=>(x-7)(x-8) = 0
=>x = 7,8
From II:
II.y^2 + 2y – 63 = 0
=>y^2 + 9y – 7y – 63 = 0
=>(y+9)(y-7)= 0
=> y = -9,7
x >= y

8. I.7x + 8y = 80
II.9x – 5y = 57

x>=y
y >= x
x > y
No relation.
y > x
Option C
On solving both the equations,we get
x = 8 y = 3
x>y

9. I.x^2 – 3x – 18 = 0
II.y^2 + 8y + 15 = 0

y >= x
x>=y
x > y
y > x
No relation.
Option B
From I:
I.x^2 – 3x – 18 = 0
=>x^2 + 3x – 6x – 18 = 0
=>(x+3)(x-6) = 0
=>x = -3,6
From II:
II.y^2 + 8y + 15 = 0
=>y^2 + 5y + 3y + 15 = 0
=>(y+3)(y+5)= 0
=>y = -3,-5
x>=y

10. I.x^2 – 2x – 15 = 0
II.y^2 + 4y – 12 = 0

x > y
No relation.
y > x
y >= x
x>=y
Option B
From I:
I.x^2 – 2x – 15 = 0
=>x^2 – 5x + 3x – 15 = 0
=>(x-5)(x+3)=0
=>x = 5,-3
From II:
II.y^2 + 4y – 12 = 0
=>y^2 + 6y – 2y – 12 = 0
=>(y+6)(y-2)= 0
=>y = -6,2
No relation.