# Quantitative Aptitude: Quadratic Equations Questions Set 57

Directions(1-10): Find the values of x and y and compare their values, then choose a correct option.

1. I. 9x² – 45x + 56 = 0
II. 4y² – 17y + 18 = 0
No relation
x ≥ y
x > y
y > x
𝑦 ≥ x
Option C
I. 9x² – 45x + 56 = 0
⇒ 9x² – 24x – 21x + 56 = 0
⇒ 3x (3x – 8) – 7 (3x – 8) = 0
⇒ (3x – 8) (3x – 7) = 0
⇒ x = 8/3, 7/3
II. 4y² – 17y + 18 = 0
⇒ 4y² – 8y – 9y + 18 = 0
⇒ (y – 2) (4y – 9) = 0
⇒ y = 2, 9/4
x > y

2. I. x² – 72 = x
II. y² = 64
𝑦 ≥ x
x > y
y > x
No relation
x ≥ y
Option D
I. x² –x – 72 = 0
x² – 9x + 8x – 72 = 0
x (x – 9) +8 (x – 9) = 0
x = 9 or -8
II. y² = 64
y = ± 8
No relation

3. I. 2x² – 7x + 3 = 0
II. 2y² – 7y + 6 = 0
x > y
𝑦 ≥ x
x ≥ y
y > x
No relation
Option E
I. 2x² – 7x + 3 = 0
⇒ 2x² – 6x – x +3 = 0
⇒ (x – 3) (2x – 1) = 0
⇒ x = 3, 1/ 2
II. 2y² – 7y +6 = 0
⇒ 2y² – 4y – 3y + 6 =0
⇒ (y – 2) (2y – 3) = 0
⇒ y = 2, 3/2
No relation

4. I. 4x² + 16x + 15 = 0
II. 2y² + 3y + 1 = 0
𝑦 ≥ x
x > y
y > x
x ≥ y
No relation
Option C
I. 4x² + 16x + 15 = 0
⇒ 4x² + 10x + 6x + 15 = 0
⇒ 2x (2x + 5) + 3 (2x + 5) = 0
⇒ (2x + 5) (2x + 3) = 0
⇒ x= -5/2, -3/2
II. 2y² + 3y + 1 = 0
⇒ 2y² + 2y + y + 1 = 0
⇒ (y + 1) (2y + 1) = 0
⇒ y = -1, -1/2
y > x

5. I. 2x² + 11x + 14 = 0
II. 2y² + 15y + 28 = 0
y > x
𝑦 ≥ x
x > y
x ≥ y
No relation
Option D
I. 2x² + 11x + 14 = 0
⇒ 2x² + 4x + 7x + 14= 0
⇒ (x + 2) (2x + 7) = 0
⇒ x = -2, -7/2
II. 2y² + 15y + 28= 0
⇒ 2y² + 8y + 7y + 28 = 0
⇒ (y + 4) (2y + 7) = 0
⇒ y = –4, –7/2
x ≥ y

6. I. 4x² – 25x + 39 = 0
II. 18y² – 15y + 3 = 0
x ≥ y
No relation
y > x
x > y
𝑦 ≥ x
Option D
I. 4x² – 25x + 39 = 0
4x² – 13x – 12x + 39 = 0
x (4x – 13) – 3 (4x – 13) = 0
𝑥 = 13/ 4 𝑜𝑟 3
II. 18y² – 15y + 3 = 0
18y² – 9y – 6y + 3= 0
9y (2y – 1) – 3 (2y – 1) = 0
𝑦 = 1 /2 𝑜𝑟 1/ 3
x > y

7. I. 6x² + 23x + 20 = 0
II. 6y² +31y + 35 = 0
𝑦 ≥ x
No relation
x ≥ y
y > x
x > y
Option B
I. 6x² + 23x + 20 = 0
6x² + 15x + 8x + 20 = 0
3x (2x + 5) +4(2x + 5) = 0
𝑥 = −5/ 2 𝑜𝑟 −4 /3
II. 6y² + 31y + 35 = 0
6y² + 21y + 10y + 35 = 0
3y (2y + 7) + 5(2y + 7) = 0
𝑦 = −7 /2 𝑜𝑟 −5/ 3
No relation

8. I. 30x² + 11x + 1 = 0
II. 42y² + 13y + 1 = 0
𝑦 ≥ x
x ≥ y
x > y
No relation
y > x
Option A
I. 30x² + 11x +1 = 0
30x² + 5x + 6x + 1= 0
5x (6x + 1) +1 (6x + 1) = 0
𝑥 = − 1 /6 or − 1 /5
II. 42y² + 13y + 1 = 0
42y² + 6y + 7y + 1 = 0
6y (7y + 1) +1 (7y + 1) = 0
𝑦 = − 1/ 7 𝑜𝑟 − 1 /6
𝑦 ≥ x

9. I. 3x + 5y = 28
II. 8x – 3y = 42
x > y
y > x
No relation
x ≥ y
𝑦 ≥ x
Option A
I. 3x + 5y = 28 …(i)
II. 8x – 3y = 42 …..(ii)
Multiplying (i) by 3 and (ii) by 5
𝑥 = 6
y = 2
x > y

10. I. 9x² – 36x + 35 = 0
II. 2y² – 15y – 17 = 0
x ≥ y
No relation
x > y
y > x
𝑦 ≥ x
Option B
I. 9x² – 36x + 35 = 0
⇒ 9x² – 21x – 15x + 35 = 0
⇒ 3x (3x – 7) -5 (3x – 7) = 0
⇒ (3x- 7) (3x – 5) = 0
⇒ 𝑥 = 5 /3 , 7/ 3
II. 2y² – 15y – 17 = 0
⇒ 2y² – 17y + 2y – 17 = 0
⇒ (y + 1) (2y – 17) = 0
⇒ y= -1, 17 /2
No relation