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a>b
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06 Jan 2022, 03:57
06 Jan 2022, 03:57
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\(a>b\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
See more on this topic Numbers Comprehension
Quantity A |
Quantity B |
\(a-b\) |
\(\sqrt{(b-a)^2}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
See more on this topic Numbers Comprehension
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Re: a>b
[#permalink]
07 Jan 2022, 06:07
07 Jan 2022, 06:07
2
Given that \(a>b\)
Quantity A = a-b
Quantity B = \(\sqrt{(b-a)^2}\)
Now, \(\sqrt{(b-a)^2}\) = \(\sqrt{(a-b)^2}\) = a-b as Square root of a number is always positive and since a > b => a-b > 0 => Positive
So, Quantity A = Quantity B = a-b
Explaining using values
Let a = 3 and b= 1
=> a-b = 3-1 = 2
\(\sqrt{(b-a)^2}\) = \(\sqrt{(1-3)^2}\) = \(\sqrt{(-2)^2}\) = \(\sqrt 4\) = 2 = a-b
So, Answer will be C
Hope it helps!
Quantity A = a-b
Quantity B = \(\sqrt{(b-a)^2}\)
Now, \(\sqrt{(b-a)^2}\) = \(\sqrt{(a-b)^2}\) = a-b as Square root of a number is always positive and since a > b => a-b > 0 => Positive
So, Quantity A = Quantity B = a-b
Explaining using values
Let a = 3 and b= 1
=> a-b = 3-1 = 2
\(\sqrt{(b-a)^2}\) = \(\sqrt{(1-3)^2}\) = \(\sqrt{(-2)^2}\) = \(\sqrt 4\) = 2 = a-b
So, Answer will be C
Hope it helps!
Re: a>b
[#permalink]
25 Jan 2022, 06:14
25 Jan 2022, 06:14
2
I understand this problem from by a conceptual method and by using plug-in, but I was also wondering why it is mathematically incorrect to have the square root cancel out the square, thereby simplifying Quantity B to (b-a).
My best explanation so far is that if one foils (b-a)^2, it would be a much different radical than (b-a). However, I would like to hear someone else's explanation as to why we can'thave the square root cancel out the square and simplify Quantity B to (b-a).
My best explanation so far is that if one foils (b-a)^2, it would be a much different radical than (b-a). However, I would like to hear someone else's explanation as to why we can'thave the square root cancel out the square and simplify Quantity B to (b-a).
