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Which is greater |x| or y
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27 Jan 2020, 10:20
27 Jan 2020, 10:20
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\(x^2=|y|\)
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
Quantity A |
Quantity B |
\(|x|\) |
\(y\) |
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
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Posts: 6218
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Which is greater |x| or y
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27 Jan 2020, 11:39
27 Jan 2020, 11:39
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Carcass wrote:
\(x^2=|y|\)
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
Quantity A |
Quantity B |
\(|x|\) |
\(y\) |
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
When I examine the given information and the two quantities, I can see some values that satisfy the given equation AND show that the two quantities are equal.
Great! There's a useful strategy called looking for equality that I can apply here
case i: Since \(x^2=|y|\), it could be the case \(x=0\) and \(y=0\)
We get:
Quantity A: \(|x|=|0|=0\)
Quantity B: \(y=0\)
In this case, the quantities are equal
Now that we've identified a case where the two quantities are equal, Let's test another set of values
case ii: Since \(x^2=|y|\), it could be the case \(x=2\) and \(y=4\)
We get:
Quantity A: \(|x|=|2|=2\)
Quantity B: \(y=4\)
In this case, Quantity B is greater
Answer: D
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Re: Which is greater |x| or y
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28 Jan 2020, 04:53
28 Jan 2020, 04:53
1
Carcass wrote:
\(x^2=|y|\)
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
Quantity A |
Quantity B |
\(|x|\) |
\(y\) |
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
We know that: \(x^2 = |y|\)
\(=> |x|^2 = |y|\)
\(=> |x| = \sqrt{|y|}\)
Thus, we need to compare:
Quantity A: \(|x| = \sqrt{|y|}\)
Quantity B: \(y\)
The various possibilities are:
#1. If \(y < 0\): Quantity A will be greater since it is positive while Quantity B is negative
#2. If \(y = 1\) or \(y = 0\): Quantity A will be equal to Quantity B, both being zero
#3. If \(0 < y < 1\): Quantity A will be greater than Quantity B since square root of a fraction is greater than the fraction itself (ex. \(\sqrt{0.49} = 0.7 > 0.49\))
#4. If \(y > 1\): Quantity B will be greater than Quantity A
Thus, there is no relation
Answer D
