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Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Quantity A: x where 4x2 - 5x + 1 = 0
Quantity B: y where y2 - 3y + 2 = 0
- a)Quantity A > Quantity B
- b)Quantity A < quantity="" />
- c)Quantity A ≥ Quantity B
- d)Quantity A ≤ Quantity B
- e)Quantity A = Quantity B OR relationship cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Directions: Given below are two quantities named A and B. Based on th...
Given information:
Quantity A: x where 4x^2 - 5x + 1 = 0
Quantity B: y where y^2 - 3y + 2 = 0
To determine the relationship between Quantity A and Quantity B, we need to solve both equations and compare the values of x and y.
Solving Quantity A equation:
4x^2 - 5x + 1 = 0
Using the quadratic formula, we have:
x = (-(-5) ± √((-5)^2 - 4(4)(1)))/(2(4))
Simplifying further:
x = (5 ± √(25 - 16))/8
x = (5 ± √9)/8
x = (5 ± 3)/8
Hence, we have two possible solutions for x:
x₁ = (5 + 3)/8 = 8/8 = 1
x₂ = (5 - 3)/8 = 2/8 = 1/4
So, Quantity A has two solutions: x = 1 and x = 1/4.
Solving Quantity B equation:
y^2 - 3y + 2 = 0
This equation can be factored as:
(y - 2)(y - 1) = 0
Hence, we have two possible solutions for y:
y₁ = 2 and y₂ = 1
Comparing the solutions:
x = 1, 1/4
y = 2, 1
From the solutions obtained, we can see that Quantity A has two distinct values (1 and 1/4), while Quantity B has two distinct values (2 and 1).
Since Quantity A has more values than Quantity B, we can conclude that Quantity A is greater than Quantity B.
Therefore, the correct answer is option D: Quantity A ≥ Quantity B.
Quantity A: x where 4x^2 - 5x + 1 = 0
Quantity B: y where y^2 - 3y + 2 = 0
To determine the relationship between Quantity A and Quantity B, we need to solve both equations and compare the values of x and y.
Solving Quantity A equation:
4x^2 - 5x + 1 = 0
Using the quadratic formula, we have:
x = (-(-5) ± √((-5)^2 - 4(4)(1)))/(2(4))
Simplifying further:
x = (5 ± √(25 - 16))/8
x = (5 ± √9)/8
x = (5 ± 3)/8
Hence, we have two possible solutions for x:
x₁ = (5 + 3)/8 = 8/8 = 1
x₂ = (5 - 3)/8 = 2/8 = 1/4
So, Quantity A has two solutions: x = 1 and x = 1/4.
Solving Quantity B equation:
y^2 - 3y + 2 = 0
This equation can be factored as:
(y - 2)(y - 1) = 0
Hence, we have two possible solutions for y:
y₁ = 2 and y₂ = 1
Comparing the solutions:
x = 1, 1/4
y = 2, 1
From the solutions obtained, we can see that Quantity A has two distinct values (1 and 1/4), while Quantity B has two distinct values (2 and 1).
Since Quantity A has more values than Quantity B, we can conclude that Quantity A is greater than Quantity B.
Therefore, the correct answer is option D: Quantity A ≥ Quantity B.
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Community Answer
Directions: Given below are two quantities named A and B. Based on th...
Quantity A:
x where 4x2 - 5x + 1 = 0
⇒ (4x - 1)(x - 1) = 0
⇒ x = 0.25 or 1
Quantity B:
y where y2 - 3y + 2 = 0
⇒ (y - 1)(y - 2) = 0
⇒ y = 2 or 1
∴ B ≥ A
Hence, the correct option is (D).
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Directions: Given below are two quantities named A and B. Based on the given information, you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.Quantity A: x where 4x2 - 5x + 1 = 0Quantity B: y where y2 - 3y + 2 = 0a)Quantity A > Quantity Bb)Quantity A c)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B OR relationship cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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