# 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

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