BANK & INSURANCE (QUADRATIC EQUATION PART 2)

Total Questions: 50

21. I. x² - 19x + 84 = 0 

II. y² - 26y + 168 = 0

Correct Answer: (e) x ≥ y
Solution:

From I:
x² - 19x + 84 = 0
x² - 12x - 7x + 84 = 0
x(x - 12) - 7(x - 12) = 0
(x - 7)(x - 12) = 0
x = 7, 12

From II:
y² - 26y + 168 = 0
y² - 14y - 12y + 168 = 0
y(y - 14) - 12(y - 14) = 0
(y - 12)(y - 14) = 0
y = 12, 14

22. I. (x - 4)² = 2x - 8 

II. y³ + 28 = 540

Correct Answer: (b) x ≤ y
Solution:

From I:
(x - 4)² = 2x - 8
x² - 8x + 16 = 2x - 8
x² - 10x + 24 = 0
x² - 4x - 6x + 24 = 0
x(x - 4) - 6(x - 4) = 0
(x - 4)(x - 6) = 0
x = 4, 6

From II:
y³ + 28 = 540
y³ = 512
y = 8

23. I. 3x² + 25 = x² + 363 

II. 4y² + 44 = y² + 719

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

From I:
3x² + 25 = x² + 363
2x² = 338
x² = 169
x = ±13

From II:
4y² + 44 = y² + 719
3y² = 675
y² = 225
y = ±15

24. I. x² + 8x + 15 = 0  

II. y² + 20y + 99 = 0

Correct Answer: (a) x < y
Solution:

From I:
x² + 8x + 15 = 0
x² + 5x + 3x + 15 = 0
x(x + 5) + 3(x + 5) = 0
(x + 3)(x + 5) = 0
x = -3, -5

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

25. I. x² - 14x - 32 = 0 

II. y² + 20y + 36 = 0

Correct Answer: (d) x > y
Solution:

From I:
x² - 14x - 32 = 0
x² + 2x - 16x - 32 = 0
x(x + 2) - 16(x + 2) = 0
(x + 2)(x - 16) = 0
x = -2, 16

From II:
y² + 20y + 36 = 0
y² + 2y + 18y + 36 = 0
y(y + 2) + 18(y + 2) = 0
(y + 2)(y + 18) = 0
y = -2, -18

26. I. x² + 24x + 128 = 0 

II. y² + 36y + 324 = 0

Correct Answer: (a) x < y
Solution:

From I:
x² + 24x + 128 = 0
x² + 16x + 8x + 128 = 0
x(x + 16) + 8(x + 16) = 0
(x + 16)(x + 8) = 0
x = -16, -8

From II:
y² + 36y + 324 = 0
y² + 18y + 18y + 324 = 0
y(y + 18) + 18(y + 18) = 0
(y + 18)(y + 18) = 0
y = -18, -18

27. I. 2x² - 23x + 38 = 0 

II. 16y + 6³ = 288

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

From I:
2x² - 23x + 38 = 0
2x² - 4x - 19x + 38 = 0
2x(x - 2) - 19(x - 2) = 0
(2x - 19)(x - 2) = 0
x = 2, 19/2

From II:
16y + 6³ = 288
16y = 288 - 216 = 72
y = 72/16 = 4.5

28. I. (x + 14)² = 100  

II. y² - 8y = 240

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

From I:
(x + 14)² = 100
x² + 28x + 196 = 100
x² + 28x + 96 = 0
x² + 24x + 4x + 96 = 0
x(x + 24) + 4(x + 24) = 0
(x + 24)(x + 4) = 0
x = -24, -4

From II:
y² - 8y = 240
y² - 8y - 240 = 0
y² + 12y - 20y - 240 = 0
y(y + 12) - 20(y + 12) = 0
(y + 12)(y - 20) = 0
y = -12, 20

29. I. 7x + 13y = 212   

II. 15y + 216 = 396

Correct Answer: (b) x ≤ y
Solution:From I:
7x + 13y = 212
7x + 13 × 12 = 212
7x = 212 - 156
7x = 56
x = 8

From II:
15y + 216 = 396
15y = 396 - 216
15y = 180
y = 12

30. I. (x - 16) = 32/(x - 12) 

II. 6y³ + 928 = 4000

Correct Answer: (d) x > y
Solution:

From I:
(x - 16) = 32/(x - 12)
x² - 28x + 192 = 32
x² - 28x + 160 = 0
x² - 20x - 8x + 160 = 0
x(x - 20) - 8(x - 20) = 0
(x - 20)(x - 8) = 0
x = 20, 8

From II:
6y³ + 928 = 4000
6y³ = 3072
y³ = 512
y = 8