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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 112

Kudos [?]: 1865 , given: 397

-(x)3 = 64 [#permalink]
Expert's post 00:00

Question Stats: 90% (00:33) correct 10% (00:10) wrong based on 30 sessions
$$-(x)^3 = 64$$

 Quantity A Quantity B $$x^4$$ $$x^5$$

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.
[Reveal] Spoiler: OA

_________________

Sandy
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Try our free Online GRE Test Intern Joined: 02 May 2018
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Re: -(x)3 = 64 [#permalink]
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KUDOS
$$-(x)^3 = 64$$ can also be viewed as this. $$-1 * (x)^3 = 64$$

From here, rewrite the equation to solve for x.

$$(x)^3 = -64$$

to be honest, I'm not quite sure you can take a cube root of -64 so that's why it's not shown. I also just happen to know that 4*4*4 is 64 so that's why I just write it as so.

$$-4^3 = -64$$

$$x= -4$$

When comparing it to the original problem at hand, we see that in Quantity A, the exponent is an even exponent while in Quantity B it is an odd one.
The exponential property is even exponents with negative integers are positive, whereas odd exponents with negative integers are negative. So without solving the equation, we can just look at the numbers and say that Quantity A is greater than Quantity B.

The correct answer is A.
GRE Instructor Joined: 10 Apr 2015
Posts: 1795
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Kudos [?]: 1681 , given: 8

Re: -(x)3 = 64 [#permalink]
Expert's post
sandy wrote:
$$-(x)^3 = 64$$

 Quantity A Quantity B $$x^4$$ $$x^5$$

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.

GIVEN: -(x)³ = 64
In other words: (-1)(x)³ = 64
Divide both sides by -1 to get: In other words: x³ = -64

KEY PROPERTY: ODD exponents PRESERVE the sign of the base.
That is, POSITIVE^ODD = POSITIVE and NEGATIVE^ODD = NEGATIVE
For example, (-2)^5 = -32 and 2^5 = 32

Conversely, EVEN exponents result in values are greater than or equal to zero.
(-2)^6 = 64, 5^4 = 625, etc

So, once we know that x³ = -64, we know that x is NEGATIVE

So, we get:
Quantity A: NEGATIVE^4
Quantity B: NEGATIVE^5

If we applies the above properties, we get:
Quantity A: POSITIVE
Quantity B: NEGATIVE

Answer: A

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails Re: -(x)3 = 64   [#permalink] 05 Sep 2018, 07:01
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