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Which is greater x^2| or |x|^2
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09 May 2015, 11:18
09 May 2015, 11:18
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Question Stats:
92% (00:20) correct
7% (00:16) wrong based on 282 sessions
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Quantity A |
Quantity B |
\(|x^2|\) |
\(|x|^2\) |
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #100
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12 May 2015, 14:36
12 May 2015, 14:36
2
sandy wrote:
Quantity A: \(|x^2|\)
Quantity B: \(|x|^2\)
Quantity B: \(|x|^2\)
The outcome of each quantity is the same.
|x²|: the x² portion already converts any value into a POSITIVE number (unless x = 0, in which case it remains 0). So, taking the absolute value of x² has no effect; the value remains positive.
|x|²: the absolute value portion converts any value into a POSITIVE number (unless x = 0, in which case it remains 0). Squaring the resulting value results in a positive number.
Let's test a few values of x:
x = 2
|x²| = |2²| = |4| = 4
|x|² = |2|² = 2² = 4
x = -3
|x²| = |-3²| = |9| = 9
|x|² = |-3|² = 3² = 9
x = 0
|x²| = |0²| = |0| = 0
|x|² = |0|² = 0² = 0
Answer:
Show: ::
C
Cheers,
Brent
Re: Which is greater x^2| or |x|^2
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28 Sep 2020, 09:03
28 Sep 2020, 09:03
|x| = \(\sqrt{(x^2)}\).
Therefore, Quantity A = \(\sqrt{(x^4)}\) = \(x^2\) and Quantity B = \((\sqrt{(x^2)})^2\) = \(x^2\).
Quantity A = Quantity B.
Correct answer is option C.
Therefore, Quantity A = \(\sqrt{(x^4)}\) = \(x^2\) and Quantity B = \((\sqrt{(x^2)})^2\) = \(x^2\).
Quantity A = Quantity B.
Correct answer is option C.
