# 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