BANK & INSURANCE (QUADRATIC EQUATION PART 2)

Total Questions: 50

41. I. x² - 3x - 54 = 0 

II. y² - 20y + 99 = 0

Correct Answer: (e) x ≥ y
Solution:

From I:
x² - 3x - 54 = 0
x² - 9x + 6x - 54 = 0
x(x - 9) + 6(x - 9) = 0
(x + 6)(x - 9) = 0
x = -6, 9

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

42. I. x² - 17x + 60 = 0 

II. y² - 22y + 112 = 0

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

From I:
x² - 17x + 60 = 0
x² - 5x - 12x + 60 = 0
x(x - 5) - 12(x - 5) = 0
(x - 12)(x - 5) = 0
x = 12, 5

From II:
y² - 22y + 112 = 0
y² - 14y - 8y + 112 = 0
y(y - 14) - 8(y - 14) = 0
(y - 8)(y - 14) = 0
y = 8, 14

43. I. x² + 56 = 380   

II. 2y³ + 24 = 3480

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

From I:
x² + 56 = 380
x² = 324
x = ±18

From II:
2y³ + 24 = 3480
2y³ = 3456
y³ = 1728
y = 12

44. I. x³ + 63 = 1394  

II. 2y² + 36 = 198

Correct Answer: (a) x < y
Solution:

From I:
x³ + 63 = 1394
x³ = 1331
x = 11

From II:
2y² + 36 = 198
y² = 81
y = ±9

45. I. x² + 19x + 84 = 0 

II. y² + 21y + 104 = 0

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

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

From II:
y² + 21y + 104 = 0
y² + 8y + 13y + 104 = 0
y(y + 8) + 13(y + 8) = 0
(y + 13)(y + 8) = 0
y = -13, -8

46. I. (x + 4)² = 16   

II. (y - 3)² = 4

Correct Answer: (b) x ≤ y
Solution:

From I:
(x + 4)² = 16
(x + 4) = ±4
x = 0, -8

From II:
(y - 3)² = 4
(y - 3) = ±2
y = 1, 5

47. I. x² = 25      

II. y² + 6y = 0

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

From I:
x² = 25
x = -5, 5

From II:
y² + 6y = 0
y(y + 6) = 0
y = 0, -6

48. I. x³ = -512     

II. y² + 21y + 108 = 0

Correct Answer: (a) x < y
Solution:

From I:
x³ = -512
x = -8

From II:
y² + 21y + 108 = 0
y² + 12y + 9y + 108 = 0
y(y + 12) + 9(y + 12) = 0
(y + 12)(y + 9) = 0
y = -12, -9

49. I. x + 5 = 12    

II. 3y + 5 = 2x

Correct Answer: (a) x < y
Solution:

From I:
(x + 5) = 12
x = 7

From II:
3y + 5 = 2x
Using I,
3y + 5 = 14
3y = 9
y = 3

50. I. x² + 2x - 48 = 0 

II. y² + 19y + 88 = 0

Correct Answer: (d) x > y
Solution:

From I:
x² + 2x - 48 = 0
x² + 8x - 6x - 48 = 0
x(x + 8) - 6(x + 8) = 0
(x + 8)(x - 6) = 0
x = -8, 6

From II:
y² + 19y + 88 = 0
y² + 8y + 11y + 88 = 0
y(y + 8) + 11(y + 8) = 0
(y + 8)(y + 11) = 0
y = -8, -11