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

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carcass
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If x > 0, what is the value of x ? [#permalink] If x > 0, what is the value of x ?   26 Jul 2017, 09:05
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If x > 0, what is the value of x ?

(1) \(x^3 – x = 0\)

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



(DS17543)
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D
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Bunuel
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Re: If x > 0, what is the value of x ? [#permalink] If x > 0, what is the value of x ?   26 Jul 2017, 09:19
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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] If x > 0, what is the value of x ?   07 Dec 2017, 11:03
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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] If x > 0, what is the value of x ?   07 Dec 2017, 11:19
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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.
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Re: If x > 0, what is the value of x ? [#permalink] If x > 0, what is the value of x ?   25 Oct 2018, 14:07
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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If x > 0, what is the value of x ? [#permalink] If x > 0, what is the value of x ?   10 Mar 2021, 05:33
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In this question we need to ask 3 questions to ourselves:
1. What do we need to find out?
x =?
2. What do we know from Question statement?
x > 0
3. What else do we need to know?
x =?
Statement 1:
\(x^3 – x = 0\)
\(x(x^2 – 1) = 0\),
x = 0 or \(x^2 -1 = 0\)
x = 0, -1 or 1.
But, x > 0, so x = 1.
Statement 1 is sufficient.
Once, we get statement 1 as sufficient, we can knock off options B, C and E. We are left with two options A and D.
Statement 2:
\(\sqrt[3]{x} – x = 0\)
\(\sqrt[3]{x} = x\)
\(x = x^3\)
\(x^3 – x = 0\)
x can be -1, 0 or 1.
But, x > 0, so x = 1.
Statement 2 is also sufficient.
So, correct option is D.
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Re: If x > 0, what is the value of x ? [#permalink] If x > 0, what is the value of x ?   31 May 2021, 15:14
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carcass wrote:
If x > 0, what is the value of x ?

(1) \(x^3 – x = 0\)

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



(DS17543)

Solution:

We need to determine the value of x given that it’s positive.

Statement One Alone:

Factoring the left hand side of the equation, we have:

x(x^2 - 1) = 0

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

x = 0 or x = 1 or x = -1

Since we are given that x > 0, we see that x must be 1. Statement one alone is sufficient.

Statement Two Alone:

Factoring the left hand side of the equation, we have:

∛x(1 - x^(2/3)) = 0

∛x(1 - x^(1/3))(1 + x^(1/3)) = 0

x = 0 or x = 1 or x = -1

Since we are given that x > 0, we see that x must be 1. Statement two alone is sufficient.

Answer: D
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Re: If x > 0, what is the value of x ? [#permalink] If x > 0, what is the value of x ?   11 Jul 2022, 23:16
Asked: If x > 0, what is the value of x ?

(1) \(x^3 – x = 0\)
x (xˆ2 - 1) = 0
Since x>0
xˆ1 - 1 = 0
xˆ2 = 1
x = 1 > 0
SUFFICIENT

(2) \(\sqrt[3]{x} - x = 0\)
\(\sqrt[3]{x} - x = 0\)
\(\sqrt[3]{x} = x > 0\)
x = 1
SUFFICIENT

IMO D
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Re: If x > 0, what is the value of x ? [#permalink] If x > 0, what is the value of x ?   29 Jul 2023, 12:54
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