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# |x^3|< 64

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|x^3|< 64 [#permalink]  08 Aug 2018, 16:12
Expert's post
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Question Stats:

69% (00:50) correct 30% (00:44) wrong based on 99 sessions
$$|x^3|< 64$$

 Quantity A Quantity B $$-x$$ $$-|x|$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: |x^3|< 64 [#permalink]  09 Aug 2018, 12:55
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Expert's post
Carcass wrote:
$$|x^3|< 64$$

 Quantity A Quantity B -x -|x|

Let's test some possible values of x

CASE 1
Since |0³| < 64, x COULD equal 0
We get:
Quantity A: -0
Quantity B: -|0|

Evaluate to get:
Quantity A: 0
Quantity B: 0
In this case, the two quantities are EQUAL

CASE 2
Since |(-1)³| < 64, x COULD equal -1
We get:
Quantity A: -(-1)
Quantity B: -|-1|

Evaluate to get:
Quantity A: 1
Quantity B: -1
In this case, Quantity A IS GREATER

Cheers,
Brent
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Re: |x^3|< 64 [#permalink]  09 Aug 2018, 15:47
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Carcass wrote:
$$|x^3|< 64$$

 Quantity A Quantity B -x -|x|

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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30 sec approach :

It's impossible to determine the sign of a variable that keeps inside the absolute value sign. X could be positive or negative. U will get know definite value of x.

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Re: |x^3|< 64 [#permalink]  10 Aug 2018, 03:38
I selected option B because -|x| = -x.

How is it the D? I still do not understand. Could anyone further explain both question and answer?

Thank you.
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Re: |x^3|< 64 [#permalink]  10 Aug 2018, 05:07
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Expert's post
ajbozdar wrote:
I selected option B because -|x| = -x.

How is it the D? I still do not understand. Could anyone further explain both question and answer?

Thank you.

It is not always the case that -|x| = -x

If x is a POSITIVE number, then -|x| = -x
For example, if x = 2, we get: -|2| = -2
Simplify to get: -2 = -2

However, if x is a NEGATIVE number, then it is NOT the case that -|x| = -x
For example, if x = -3, we get: -|-3| = -(-3)
Simplify to get: -3 = 3, which is NOT TRUE

Does that help?

Cheers,
Brent
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If you enjoy my solutions, you'll like my GRE prep course.

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Re: |x^3|< 64 [#permalink]  10 Aug 2018, 06:25
GreenlightTestPrep wrote:

However, if x is a NEGATIVE number, then it is NOT the case that -|x| = -x
For example, if x = -3, we get: -|-3| = -(-3)
Simplify to get: -3 = 3, which is NOT TRUE

Does that help?

I have learnt that any negative number under mod becomes positive.

If so, -|-3| = -(3) i.e. = -3

Did I learn the wrong concept of absolute value?
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Re: |x^3|< 64 [#permalink]  10 Aug 2018, 08:13
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Expert's post
ajbozdar wrote:
GreenlightTestPrep wrote:

However, if x is a NEGATIVE number, then it is NOT the case that -|x| = -x
For example, if x = -3, we get: -|-3| = -(-3)
Simplify to get: -3 = 3, which is NOT TRUE

Does that help?

I have learnt that any negative number under mod becomes positive.

If so, -|-3| = -(3) i.e. = -3

Did I learn the wrong concept of absolute value?

You learned the correct concept.
In my solution, you'l see that I also state that -|-3| = -(3) = -3

Cheers,
Brent
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If you enjoy my solutions, you'll like my GRE prep course.

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Re: |x^3|< 64 [#permalink]  21 Oct 2018, 00:39
Expert's post
Yes.

Regards
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Re: |x^3|< 64 [#permalink]  23 Oct 2018, 08:43
Re: |x^3|< 64   [#permalink] 23 Oct 2018, 08:43
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