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# –(x)3 = 64

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–(x)3 = 64 [#permalink]  23 Jun 2018, 12:03
Expert's post
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Question Stats:

84% (00:22) correct 15% (00:09) wrong based on 78 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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Re: –(x)3 = 64 [#permalink]  29 Jun 2018, 06:04
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.

Here:

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

or -x = 4
or x = -4

In Quantity A : $$x^4$$= $$(-4)^4$$ = 256

In Quantity B: $$x^5$$= $$(-4)^5$$ = -1024

Hence Quantity A > Quantity B
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Re: –(x)3 = 64 [#permalink]  09 Jul 2018, 18:41
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.

Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2914 [0], given: 394

Re: –(x)3 = 64 [#permalink]  16 Jul 2018, 06:57
Expert's post
Explanation

First, solve for x:

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

The GRE calculator will not do a cube root. As a result, cube roots on the GRE tend to be quite small and easy to puzzle out. What number times itself three times equals –64? The answer is x = –4.

Since x is negative, Quantity A is positive (a negative number times itself four times is positive) and Quantity B is negative (a negative number times itself five times is negative). No further calculations are needed to conclude that Quantity A is greater.

Notice that solving for the value of x here was not strictly necessary. Knowing that the cube root of a negative number is negative gives you all the information you need to solve.
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Re: –(x)3 = 64 [#permalink]  27 Apr 2020, 19:02
We know, −(x)^3=64
=> x=-4 (x is negative)
(negative x)^(even number) = always positive
(negative x)^(odd number) = always negative

so (negative x)^4 > (negative x)^5
Quantity A will be greater
Re: –(x)3 = 64   [#permalink] 27 Apr 2020, 19:02
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