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

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Bunuel
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What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink] New post   12 Oct 2017, 23:21
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What is the value of x?

(1) x^6 = 729
(2) x^5 < x^4
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C
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What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink] New post   13 Oct 2017, 08:28
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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.
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Re: What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink] New post   13 Oct 2017, 00:21
(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.

Answer C.
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What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink] New post   13 Oct 2017, 11:19
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] New post   27 Nov 2017, 19:13
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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.

Answer: C
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Re: What is the value of x? (1) x^6 = 729 (2) x^5 < x^4 [#permalink]
27 Nov 2017, 19:13
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Bunuel
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