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-|-x| or -(x)

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Carcass
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-|-x| or -(x) [#permalink] New post   25 May 2021, 19:54
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\(x \neq 0\)

Quantity A
Quantity B
\(-|-x|\)
\(-(x)\)



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.

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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D
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Re: -|-x| or -(x) [#permalink] New post   26 May 2021, 00:07
2
x = 1 :: Qt A = Qt B

x = -1 :: Qt A < Qt B

Answer D
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Re: -|-x| or -(x) [#permalink] New post   29 Dec 2021, 02:36
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Given that \(x \neq 0\)

Now let's take two cases

Case 1: x is positive number
Let's take x = 1

Quantity A = -|-x| = -|-1| = -1
Quantity B = -(x) = -(1) = -1
=> Quantity A = Quantity B

Case 2: x is negative number
Let's take x = -1

Quantity A = -|-x| = -|-(-1)| = -|1| = -1
Quantity B = -(x) = -(-1) = 1
=> Clearly two Quantities are not equal
So, we cannot say for sure if Quantity B is bigger or is equal to Quantity A

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

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Re: -|-x| or -(x) [#permalink] New post   03 Jan 2024, 01:26
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if \(x \neq 0\), then \(x\) can be positive or negative.

\(|-x|\) will always be positive, irrespective of the sign of \(x\). So quantity A is always negative.

\(-(x)\) may be positive or negative depending on the sign of \(x\). So quantity B is either positive or negative.

Hence, sometimes Quantity A is greater than Quantity B and at other times Quantity B is greater than Quantity A. Thus there is no definable relationship between them.

The Answer is Choice D.
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Re: -|-x| or -(x) [#permalink]
03 Jan 2024, 01:26
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