If x 0, what is the value of x ?

Question

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

(1)  x^3 – x = 0

(2)  \sqrt {x} - x = 0

(DS17543)

Bunuel · Accepted Answer

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 {x} - x = 0

\sqrt {x} =x

x = x^3

x^3 – x = 0 .

The same as in (1). Sufficient.

Answer: D.

sadikabid27 · Answer

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".

Bunuel · Answer

(2)  \sqrt {x} - x = 0

\sqrt {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.

Salsanousi · Answer

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

MarmikUpadhyay · Answer

Posted from my mobile device   
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 {x} – x = 0 
 \sqrt {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.

ScottTargetTestPrep · Answer

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

Kinshook · Answer

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 {x} - x = 0 
 \sqrt {x} - x = 0 
 \sqrt {x} = x > 0 
x = 1
SUFFICIENT

IMO D

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

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