BANK & INSURANCE (QUADRATIC EQUATION PART 3)

Total Questions: 50

21. I. (x + 2)² = 15x - 26

II. (y - 6)² = 6 - y

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

From I:
(x + 2)² = 15x - 26
x² + 4x + 4 = 15x - 26
x² - 11x + 30 = 0
x² - 5x - 6x + 30 = 0
x(x - 5) - 6(x - 5) = 0
(x - 5)(x - 6) = 0
x = 5, 6

From II:
(y - 6)² = 6 - y
y² - 12y + 36 = 6 - y
y² - 11y + 30 = 0
y² - 5y - 6y + 30 = 0
y(y - 5) - 6(y - 5) = 0
(y - 5)(y - 6) = 0
y = 5, 6

22. I. x² = 144      

II. y² + 12y = 0

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

From I:
x² = 144
x = -12, 12

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

23. I. x³ = -1331   

II. y² + 23y + 132 = 0

Correct Answer: (d) x ≥ y
Solution:

From I:
x³ = -1331
x = -11

From II:
y² + 23 + 132 = 0
y² + 11y + 12y + 132 = 0
y(y + 11) + 12(y + 11) = 0
(y + 11)(y + 12) = 0
y = -11, -12

24. I. 8x + 5y = 152   

II. 18y = 144

Correct Answer: (a) x > y
Solution:

From II:
18y = 144
y = 8

From I:
8x + 5y = 152
8x + 40 = 152
8x = 112
x = 14

25. I. x² + 7x = 60   

II. y² + 19y + 84 = 0

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

From I:
x² + 7x = 60
x² + 7x - 60 = 0
x² + 12x - 5x - 60 = 0
x(x + 12) - 5(x + 12) = 0
(x + 12)(x - 5) = 0
x = -12, 5

From II:
y² + 19y + 84 = 0
y² + 12y + 7y + 84 = 0
y(y + 12) + 7(y + 12) = 0
(y + 12)(y + 7) = 0
y = -12, -7

26. I. 20x² - 43x + 21 = 0

II. 5y² - 17y + 14 = 0

Correct Answer: (e) x ≤ y
Solution:

From I:
20x² - 43x + 21 = 0
20x² - 15x - 28x + 21 = 0
5x(4x - 3) - 7(4x - 3) = 0
(5x - 7)(4x - 3) = 0
x = 7/5, 3/4
x = 1.4, 0.75

From II:
5y² - 17y + 14 = 0
5y² - 10y - 7y + 14 = 0
5y(y - 2) - 7(y - 2) = 0
(5y - 7)(y - 2) = 0
y = 7/5, 2
y = 1.4, 2

27. I. x² + 2x - 168 = 0

II. y² + 5y - 204 = 0

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

From I:
x² + 2x - 168 = 0
x² - 12x + 14x - 168 = 0
x(x - 12) + 14(x - 12) = 0
(x + 14)(x - 12) = 0
x = -14, 12

From II:
y² + 5y - 204 = 0
y² - 12y + 17y - 204 = 0
y(y - 12) + 17(y - 12) = 0
(y + 17)(y - 12) = 0
y = -17, 12

28. I. x² + 38x + 361 = 0 

II. y² + 29y + 190 = 0

Correct Answer: (e) x ≤ y
Solution:

From I:
x² + 38x + 361 = 0
x² + 19x + 19x + 361 = 0
x(x + 19) + 19(x + 19) = 0
(x + 19)(x + 19) = 0
x = -19

From II:
y² + 29y + 190 = 0
y² + 10y + 19y + 190 = 0
y(y + 10) + 19(y + 10) = 0
(y + 10)(y + 19) = 0
y = -10, -19

29. I. x + 8√x + 15 = 0  

II. y + 7√y + 12 = 0

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

From I:
x + 8√x + 15 = 0
x + 3√x + 5√x + 15 = 0
√x(√x + 3) + 5(√x + 3) = 0
(√x + 3)(√x + 5) = 0
√x = -3, -5
x = 9, 25

From II:
y + 7√y + 12 = 0
y + 3√y + 4√y + 12 = 0
√y(√y + 3) + 4(√y + 3) = 0
(√y + 3)(√y + 4) = 0
√y = -3, -4
y = 9, 16

30. I. x² - 27x + 176 = 0 

II. y² - 37y + 340 = 0

Correct Answer: (b) x < y
Solution:

From I:
x² - 27x + 176 = 0
x² - 16x - 11x + 176 = 0
x(x - 16) - 11(x - 16) = 0
(x - 16)(x - 11) = 0
x = 16, 11

From II:
y² - 37y + 340 = 0
y² - 17y - 20y + 340 = 0
y(y - 20) - 17(y - 20) = 0
(y - 17)(y - 20) = 0
y = 17, 20