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# -(x)3 = 64

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Retired Moderator
Joined: 07 Jun 2014
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-(x)3 = 64 [#permalink]  20 May 2018, 11:02
Expert's post
00:00

Question Stats:

75% (00:23) correct 24% (00:20) wrong based on 79 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

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Sandy
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Joined: 02 May 2018
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Kudos [?]: 31 [1] , given: 22

Re: -(x)3 = 64 [#permalink]  30 Jul 2018, 22:51
1
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.

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Re: -(x)3 = 64 [#permalink]  05 Sep 2018, 07:01
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

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Re: -(x)3 = 64   [#permalink] 05 Sep 2018, 07:01
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