# Quantitative Aptitude: Quadratic Equations Questions Set 55

Directions(1-5): What will be the values of x and y and chose a correct option.

1. I.63x – 94√x +35=0
II. 32y – 52√y + 21=0
y>=x
x>y
x>=y
y>x
No Relation
Option E
I.63x – 94√x +35=0
II. 32y – 52√y + 21=0
√x = 7/9 , 5/7
x = 49/ 81 , 25/ 49
√y = 3 /4 , 7 /8
y = 9 /16 , 49 /64
No Relation

2. I. 2x² + 17x + 35 = 0
II. 3y² + 17y + 24 = 0
x>y
y>=x
x>=y
No Relation
y>x
Option E
I. 2x² + 17x + 35 = 0
2x² + 10x+ 7x + 35 = 0
2x (x+ 5) +7 (x+ 5) = 0
(2x+ 7) (x+ 5) =0
x = (-7)/2, -5
II. 3y² + 17y + 24 = 0
3y² + 9y + 8y + 24 = 0
3y (y + 3) + 8 (y+ 3) = 0
(y+ 3) (3y + 8) = 0
y= -3, -8/3
y > x

3. I.x² – 17x + 72 = 0
II.y² – 27y + 180 = 0
x>y
No Relation
x>=y
y>x
y>=x
Option D
I.x² – 17x + 72 = 0
x² – 9x – 8x + 72 = 0
x(x – 9) – 8 (x – 9) = 0
(x – 8) (x – 9) = 0
x = 8, 9
II. y² – 27y + 180 = 0
y² – 12y – 15y + 180 = 0
y(y – 12) – 15 (y – 12) = 0
(y – 15) (y – 12) = 0
y = 15, 12
y > x

4. I. 2x² – 5x + 3 = 0
II. 3y² – 4y + 1 = 0
y>=x
x>y
No Relation
x>=y
y>x
Option D
I.2x² – 5x + 3 = 0
2x² – 2x – 3x + 3 = 0
2x (x – 1) – 3(x – 1) = 0
(x – 1) (2x – 3) = 0
x = 1, 3 /2
II. 3y² – 4y + 1 = 0
3y² – 3y – y + 1 = 0
3y(y – 1) –1 (y – 1) = 0
(3y – 1) (y – 1) = 0
𝑦 = 1/3 , 1
x≥y

5. I. x² + 2x – 35 = 0
II. y² + 15y + 56 = 0
y>=x
x>=y
x>y
y>x
No Relation
Option B
I.x² + 2x – 35 = 0
x² + 7x – 5x – 35 = 0
x (x + 7) – 5 (x + 7) = 0
(x – 5) (x + 7) = 0
x = 5, –7
II. y² + 15y + 56 = 0
y² + 7y + 8y + 56 = 0
y (y + 7) + 6 (y + 7) = 0
(y + 8) (y + 7) = 0
y = – 8, – 7
x ≥ y

6. I. 2x² + 7x + 5 = 0
II.3y² + 12y + 9 = 0
y>=x
x>y
y>x
x>=y
No Relation
Option E
I.2x² + 7x + 5 = 0
2x² + 2x + 5x + 5 = 0
2x (x + 1) + 5 (x + 1) = 0
(2x + 5) (x + 1) = 0
𝑥 = – 5/2 , – 1
II.3y² + 12y + 9 = 0
3y² + 9y + 3y + 9 = 0
3y (y + 3) +3 (y + 3) = 0
(3y + 3) (y + 3) = 0
y = –1, – 3
No relation

7. I. (x – 12)² = 0
II.y² – 21y + 108 = 0
x>y
y>=x
x>=y
No Relation
y>x
Option C
I.(x – 12)² = 0
x – 12 = 0
x = 12
II. y² – 21y + 108 = 0
y² – 12y – 9y + 108 = 0
y (y – 12) – 9 (y – 12) = 0
(y – 9) (y – 12) = 0
y = 9, 12
x ≥ y

8. I. x² + 72 = 108
II. y³ + 581 = 365
x>=y
y>=x
x>y
y>x
No Relation
Option A
I. x² + 72 = 108
x² =108 – 72 = 36
x = ±6
II. y³ + 581 = 365
y³ = –216
y = –6
x ≥ y

9. I. 8x² + 26x + 15 = 0
II. 4y² + 24y + 35 = 0
y>=x
y>x
x>y
x>=y
No Relation
Option D
I. 8x² + 26x + 15 = 0
8x^2 + 20x +6x + 15 = 0
4(2x+5)+3(2x+5) = 0
x = -5/2,-3/4
II. 4y² + 24y + 35 = 0
4y^2 + 10y + 14 y + 35 = 0
y = -5/2,-7/2
x >= y

10. I. 15x^2 – 46x+35
II. 4y^2 – 15y+14=0
x>y
y>=x
x>=y
y>x
No Relation
Option D
x = 7/5, 5/3
Y = 2, 7/4
x < y

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