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# What is the value of x? (1) x^6 = 729 (2) x^5 < x^4

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Math Expert
Joined: 02 Sep 2009
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What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink]

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12 Oct 2017, 22:21
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What is the value of x?

(1) x^6 = 729
(2) x^5 < x^4
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135380 [1], given: 12691

Manager
Joined: 05 Dec 2016
Posts: 248

Kudos [?]: 26 [0], given: 49

Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink]

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12 Oct 2017, 23:21
(1) Prime factorization shows that x^6=|3|^6, so x can take either -3 or 3
(2) insufficient, no info about value of x

(1)+(2)
x^5<x^4 ====> means that x is negative so x= -3.

Kudos [?]: 26 [0], given: 49

Intern
Joined: 25 Jul 2017
Posts: 18

Kudos [?]: 22 [1], given: 44

What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink]

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13 Oct 2017, 07:28
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1/ x^6= 729. We have (-3)^6 = (3)^6 = 729 => cannot decide => insuff

2/ x^5<x^4 => X is negative => insuff

Combine 1 and 2 => x=-3 => Answer C

Please kudo if it helps. Thanks.

Kudos [?]: 22 [1], given: 44

Manager
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What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink]

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13 Oct 2017, 10:19
Bunuel wrote:
What is the value of x?

(1) x^6 = 729
(2) x^5 < x^4

It should be C

1- $$x^6 = 729$$

$$|x| = 3$$ i.e. $$x = +3$$ $$or -3$$

-- Insufficient

2- $$x^5 < x^4$$

$$x^5 - x^4 < 0$$
$$x^4 (x - 1) < 0$$

Either

$$x^4 < 0$$ - impossible
or
$$x - 1 < 0$$
i.e. $$x < 1$$ but this gives us a range of values.

Combining $$1$$ and $$2$$, only value of x less than $$1$$ is $$-3$$. Hence answer is C
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Re: What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink]

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27 Nov 2017, 18:13
Bunuel wrote:
What is the value of x?

(1) x^6 = 729
(2) x^5 < x^4

Statement One Alone:

x^6 = 729

Since x^6 = 729, x = 3 or x = -3. Thus, statement one is not enough information to determine the value of x.

Statement Two Alone:

x^5 < x^4

The information in statement two does not allow for a determination of the value of x.

Statements One and Two Together:

Using the information from both statements, we see that x must be -3 since if x = 3, then x^5 > x^4.

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Jeffery Miller

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Kudos [?]: 980 [0], given: 5

Re: What is the value of x? (1) x^6 = 729 (2) x^5 < x^4   [#permalink] 27 Nov 2017, 18:13
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