BANK & INSURANCE (QUADRATIC EQUATION PART 3)

Total Questions: 50

1. I. x² - 12x + 35 = 0

II. y² - 20y + 99 = 0

Correct Answer: (b) x < y
Solution:

From I:
x² - 12x + 35 = 0
x² - 7x - 5x + 35 = 0
x(x - 7) - 5(x - 7) = 0
(x - 7)(x - 5) = 0
x = 7, 5

From II:
y² - 20y + 99 = 0
y² - 9y - 11y + 99 = 0
y(y - 9) - 11(y - 9) = 0
(y - 11)(y - 9) = 0
y = 11, 9

2. I. x² - y² = 108  

II. x + y = 18

Correct Answer: (a) x > y
Solution:From I:
x² - y² = 108
(x + y)(x - y) = 108
18 × (x - y) = 108
(x - y) = 6

From II:
x + y = 18


x > y

3. I. 9x² - 9x + 2 = 0 II. 25y² - 25y + 6 = 0

II. 25y² - 25y + 6 = 0

Correct Answer: (c) x = y or No relation
Solution:

From I:
9x² - 9x + 2 = 0
x² - x + 2/9 = 0
x² - (2x/3) - (x/3) + (2/9) = 0
x(x - 2/3) - (1/3)(x - 2/3) = 0
(x - 2/3)(x - 1/3) = 0
x = 2/3, 1/3

From II:
25y² - 25y + 6 = 0
y² - y + (6/25) = 0
y² - (2y/5) - (3y/5) + (6/25) = 0
y(y - 2/5) - (3/5)(y - 2/5) = 0
(y - 3/5)(y - 2/5) = 0
y = 3/5, 2/5

4. I. x² + 17x - 84 = 0 

II. y² + 12y - 160 = 0

Correct Answer: (c) x = y or No relation
Solution:

From I:
x² + 17x - 84 = 0
x² - 4x + 21x - 84 = 0
x(x - 4) + 21(x - 4) = 0
x + 21)(x - 4) = 0
x = -21, 4

From II:
y² + 12y - 160 = 0
y² - 8y + 20y - 160 = 0
y(y - 8) + 20(y - 8) = 0
y + 20)(y - 8) = 0
y = -20, 8

5. I. x² + 23x + 130 = 0 

II. y² + 7y + 12 = 0

Correct Answer: (b) x < y
Solution:

From I:
x² + 23x + 130 = 0
x² + 13x + 10x + 130 = 0
x(x + 13) + 10(x + 13) = 0
(x + 13)(x + 10) = 0
x = -13, -10

From II:
y² + 7y + 12 = 0
y² + 4y + 3y + 12 = 0
y(y + 4) + 3(y + 4) = 0
(y + 3)(y + 4) = 0
y = -3, -4

6. I. x² - 12x - 64 = 0 

II. y² - 15y - 54 = 0

Correct Answer: (c) x = y or No relation
Solution:

From I:
x² - 12x - 64 = 0
x² - 16x + 4x - 64 = 0
x(x - 16) + 4(x - 16) = 0
x + 4)(x - 16) = 0
Or, x = -4, 16

From II:
y² - 15y - 54 = 0
y² + 3y - 18y - 54 = 0
y(y + 3) - 18(y + 3) = 0
y - 18)(y + 3) = 0
y = 18, -3

7. I. x² + x - 72 = 0 

II. y² - y - 56 = 0

Correct Answer: (c) x = y or No relation
Solution:

From I:
x² + x - 72 = 0
x² - 8x + 9x - 72 = 0
x(x - 8) + 9(x - 8) = 0
(x + 9)(x - 8) = 0
x = -9, 8

From II:
y² - y - 56 = 0
y² + 7y - 8y - 56 = 0
y(y + 7) - 8(y + 7) = 0
(y - 8)(y + 7) = 0
y = 8, -7

8. I. x² - 78 = 91   

II. y² + 121 = 377

Correct Answer: (c) x = y or No relation
Solution:

From I:
x² - 78 = 91
x² = 169
x = ±13

From II:
y² + 121 = 377
y² = 256
y = ±16

9. I. x² = (14)²    

II. y³ + 29 = 3404

Correct Answer: (b) x < y
Solution:

From I:
x² = (14)²
x² - 196 = 0
x = ±14

From II:
y³ + 29 = 3404
y³ = 3375
y = 15

10. I. x² + 22x + 112 = 0 

II. y² + 31y + 238 = 0

Correct Answer: (d) x ≥ y
Solution: From I:
x² + 22x + 112 = 0
x² + 8x + 14x + 112 = 0
x(x + 8) + 14(x + 8) = 0
(x + 14)(x + 8) = 0
x = -14, -8

From II:
y² + 31y + 238 = 0
y² + 14y + 17y + 238 = 0
y(y + 14) + 17(y + 14) = 0
(y + 14)(y + 17) = 0
y = -14, -17