BANK & INSURANCE (QUADRATIC EQUATION PART 2)

Total Questions: 50

11. I. 14x² - 43x + 33 = 0 

II. 8y² - 29y + 26 = 0

Correct Answer: (b) x ≤ y
Solution:

From I:
14x² - 43x + 33 = 0
14x² - 22x - 21x + 33 = 0
2x(7x - 11) - 3(7x - 11) = 0
(2x - 3)(7x - 11) = 0
x = 3/2, 11/7

From II:
8y² - 29y + 26 = 0
8y² - 13y - 16y + 26 = 0
y(8y - 13) - 2(8y - 13) = 0
(8y - 13)(y - 2) = 0
y = 13/8, 2

12. I. 18x + 15y = 492   

II. y² = 256, y > 0

Correct Answer: (b) x ≤ y
Solution:

From I:
18x + 15y = 492

From II:
y² = 256
y = 16, -16
Since, y > 0
So, y = 16
Therefore, 18x + 15 × 16 = 492
18x = 492 - 240
18x = 252
x = 14

13. I. x² - 23x + 132 = 0 

II. y² - 19y + 88 = 0

Correct Answer: (d) x > y
Solution:

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

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

14. I. x² - 31x + 184 = 0 

II. y² - 49y + 600 = 0

Correct Answer: (b) x ≤ y
Solution:

From I:
x² - 31x + 184 = 0
x² - 23x - 8x + 184 = 0
x(x - 23) - 8(x - 23) = 0
(x - 23)(x - 8) = 0
x = 23, 8

From II:
y² - 49y + 600 = 0
y² - 24y - 25y + 600 = 0
y(y - 24) - 25(y - 24) = 0
(y - 24)(y - 25) = 0
y = 24, 25

15. I. 11x + 7y = 162   

II. 5x + 15y = 180

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

From I:
11x + 7y = 162
x = (162 - 7y)/11

From II:
5 × {(162 - 7y)/11} + 15y = 180
810 - 35y + 165y = 1980
130y = 1170
y = 9

16. I. x² - 11x + 18 = 0  

II. y² - 10y + 24 = 0

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

From I:
x² - 11x + 18 = 0
x² - 2x - 9x + 18 = 0
x(x - 2) - 9(x - 2) = 0
(x - 9)(x - 2) = 0
x = 9, 2

From II:
y² - 10y + 24 = 0
y² - 4y - 6y + 24 = 0
y(y - 4) - 6(y - 4) = 0
(y - 4)(y - 6) = 0
y = 4, 6

17. I. 4x + 9y = 91    

II. 9x - 4y = 35

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

From I:
4x + 9y = 91
4x = 91 - 9y
x = (91 - 9y)/4

From II:
9x - 4y = 35
9 × {(91 - 9y)/4} - 4y = 35
819 - 81y - 16y = 140
97y = 679
y = 7

18. I. x² - x - 42 = 0  

II. y² + 15y + 54 = 0

Correct Answer: (d) x > y
Solution:

From I:
x² - x - 42 = 0
x² - 7x + 6x - 42 = 0
x(x - 7) + 6(x - 7) = 0
(x - 7)(x + 6) = 0
x = 7, -6

From II:
y² + 15y + 54 = 0
y² + 9y + 6y + 54 = 0
y(y + 9) + 6(y + 9) = 0
(y + 9)(y + 6) = 0
y = -6, -9

19. I. x² + 19x + 88 = 0 

II. y² + 20y + 96 = 0

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

From I:
x² + 19x + 88 = 0
x² + 11x + 8x + 88 = 0
x(x + 11) + 8(x + 11) = 0
(x + 8)(x + 11) = 0
x = -8, -11

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

20. I. x² - 25x + 156 = 0 

II. y² - 27y + 180 = 0

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

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

From II:
y² - 27y + 180 = 0
y² - 15y - 12y + 180 = 0
y(y - 15) - 12(y - 15) = 0
(y - 15)(y - 12) = 0
y = 12, 15