BANK & INSURANCE (QUADRATIC EQUATION PART 3)

Total Questions: 50

41. I. x² - 25x + 156 = 0 

II. y² - 20y + 96 = 0

Correct Answer: (d) x ≥ y
Solution:

From I,
x² - 25x + 156 = 0
x² - 12x - 13x + 156 = 0
x(x - 12) - 13(x - 12) = 0
(x - 12)(x - 13) = 0
x = 12, 13

From II,
y² - 20y + 96 = 0
y² - 12y - 8y + 96 = 0
y(y - 12) - 8(y - 12) = 0
(y - 8)(y - 12) = 0
y = 8, 12

42. I. x² + 23x + 132 = 0

II. y² + y - 56 = 0

Correct Answer: (b) x < y
Solution:

From I,
x² + 23x + 132 = 0
x² + 12x + 11x + 132 = 0
x(x + 12) + 11(x + 12) = 0
(x + 12)(x + 11) = 0
x = -11, -12

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

43. I. x² - 11x + 28 = 0 

II. y² - 13y + 40 = 0

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

From I:
x² - 11x + 28 = 0
x² - 7x - 4x + 28 = 0
x(x - 7) - 4(x - 7) = 0
(x - 7)(x - 4) = 0
x = 4, 7

From II:
y² - 13y + 40 = 0
y² - 8y - 5y + 40 = 0
y(y - 8) - 5(y - 8) = 0
(y - 8)(y - 5) = 0
y = 5, 8

44. I. 3x + 7y = 96    

II. 9x - 4y = 63

Correct Answer: (a) x > y
Solution:

From I:
3x + 7y = 96
3x = 96 - 7y
x = (96 - 7y)/3

From II:
9x - 4y = 63
9 × {(96 - 7y)/3} - 4y = 63
864 - 63y - 12y = 189
75y = 675, y = 9
Now x = (96 - 7 × 9)/3
x = 33/3, x = 11

45. I. 3x² - 10x + 3 = 0  

II. y² - y - 12 = 0

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

From I:
3x² - 10x + 3 = 0
3x² - x - 9x + 3 = 0
x(3x - 1) - 3(3x - 1) = 0
(x - 3)(3x - 1) = 0
x = 3, 1/3

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

46. I. x² + 9x + 18 = 0  

II. y² + 2y - 15 = 0

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

Equation I

x² + 9x + 18 = 0

x² + 6x + 3x + 18 = 0

x(x + 6) + 3(x + 6) = 0

(x + 6)(x + 3) = 0

x = −6, −3

Equation II

y² + 2y − 15 = 0

y² + 5y − 3y − 15 = 0

y(y + 5) − 3(y + 5) = 0

(y − 3)(y + 5) = 0

y = 3, −5

Final Answer: (c) x = y or No relation

47. I. 2x² + 5x + 3 = 0  

II. y² - y - 2 = 0

Correct Answer: (e) x ≤ y
Solution:

From 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

From II:
y² - y - 2 = 0
y² + y - 2y - 2 = 0
y(y + 1) - 2(y + 1) = 0
(y + 1)(y - 2) = 0
y = -1, 2

48. I. x² + 3x - 28 = 0  

II. y² - 12y + 35 = 0

Correct Answer: (a) x < y
Solution:

From I:
x² + 3x - 28 = 0
x² - 4x + 7x - 28 = 0
x(x - 4) + 7(x - 4) = 0
(x - 4)(x + 7) = 0
x = 4, -7

From II:
y² - 12y + 35 = 0
y² - 7y - 5y + 35 = 0
y(y - 7) - 5(y - 7) = 0
(y - 7)(y - 5) = 0
y = 5, 7

49. I. 5x + 3y = 102   

II. 8x - 5y = 26

Correct Answer: (a) x < y
Solution:

From I:
5x + 3y = 102
5x = 102 - 3y
x = (102 - 3y)/5

From II:
8x - 5y = 26
8 × {(102 - 3y)/5} - 5y = 26
816 - 24y - 25y = 130
49y = 686
y = 14
Now, x = (102 - 14 × 3)/5
x = 60/5 = 12

50. I. 5x² - 18x + 16 = 0 

II. 6y² = y + 12

Correct Answer: (d) x > y
Solution:

From I:
5x² - 18x + 16 = 0
5x² - 10x - 8x + 16 = 0
5x(x - 2) - 8(x - 2) = 0
(5x - 8)(x - 2) = 0
x = 2, 8/5

From II:
6y² = y + 12
6y² - y - 12 = 0
6y² - 9y + 8y - 12 = 0
3y(2y - 3) + 4(2y - 3) = 0
(2y - 3)(3y + 4) = 0
y = -4/3, 3/2