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If x > 0, what is the value of x ?

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If x > 0, what is the value of x ?  [#permalink]

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New post 26 Jul 2017, 08:05
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Re: If x > 0, what is the value of x ?  [#permalink]

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New post 26 Jul 2017, 08:19
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1
If x > 0, what is the value of x ?


(1) \(x^3 – x = 0\). Since x is not 0, we can safely reduce by x:

\(x^2 - 1 = 0\)

\(x^2 = 1\)

\(x = 1\) or \(x = -1\) (discard since \(x > 0\)).

So, \(x = 1\) only. Sufficient.


(2) \(\sqrt[3]{x} - x = 0\)

\(\sqrt[3]{x} =x\)

\(x = x^3\)

\(x^3 – x = 0\).

The same as in (1). Sufficient.

Answer: D.
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Re: If x > 0, what is the value of x ?  [#permalink]

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New post 07 Dec 2017, 10:03
Dear Bunuel can you please clarify "^3√x=x, then x=x^3" how the interchange occurred? and I had x=1 in the statement 1 which made that sufficient, but what value do Statement 2 has to make it sufficient? Not getting this part in statement 2 "x^3–x=0. The same as in (1). Sufficient".
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Re: If x > 0, what is the value of x ?  [#permalink]

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New post 07 Dec 2017, 10:19
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sadikabid27 wrote:
Dear Bunuel can you please clarify "^3√x=x, then x=x^3" how the interchange occurred? and I had x=1 in the statement 1 which made that sufficient, but what value do Statement 2 has to make it sufficient? Not getting this part in statement 2 "x^3–x=0. The same as in (1). Sufficient".


(2) \(\sqrt[3]{x} - x = 0\)

\(\sqrt[3]{x} =x\)

Take to the third power: \(x = x^3\)

\(x^3 – x = 0\). Since x is not 0, we can safely reduce by x:

\(x^2 - 1 = 0\)

\(x^2 = 1\)

\(x = 1\) or \(x = -1\) (discard since \(x > 0\)).

So, \(x = 1\) only. Sufficient.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x > 0, what is the value of x ?  [#permalink]

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New post 25 Oct 2018, 13:07
carcass wrote:
If x > 0, what is the value of x ?

(1) \(x^3 – x = 0\)

(2) \(\sqrt[3]{x} - x = 0\)



(DS17543)



This is basically Tautology in which the statements are repeated and yield the same answer.

\(x^3 - x = 0\)

\(x ( x^2 - 1) = 0\)

\(x ( x - 1) (x + 1) = 0\)

x > 0 so it can be -1 or 0 x = 1

For statement 2)

We square both sides we get \(x^3 - x = 0\)

Then the same goes on.

Answer choice D
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Re: If x > 0, what is the value of x ? &nbs [#permalink] 25 Oct 2018, 13:07
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