x=?

[Max@Math Revolution]

[Math Revolution GMAT math practice question]

x=?

1) x^3-x=0
2) x=-x

[fskilnik@GMATH]

[Math Revolution GMAT math practice question]

x=?

1) x^3-x=0
2) x=-x

$$? = x$$
$$\left( 1 \right)\,\,0 = {x^3} - x = x\left( {{x^2} - 1} \right) = x\left( {x - 1} \right)\left( {x + 1} \right)\,\,\,\, \Rightarrow \,\,\,\,x = - 1,0\,\,{\rm{or}}\,\,1\,\,\,\, \Rightarrow \,\,\,\,{\rm{INSUFF}}.$$
$$\left( 2 \right)\,\,x = - x\,\,\,\, \Rightarrow \,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$

The correct answer is therefore (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

[Brent@GMATPrepNow]

What is the value of x?

1) x³ - x = 0
2) x = -x

Target question: What is the value of x?

Statement 1: x³ - x = 0
Factor to get: x(x² - 1) = 0
Factor again to get: x(x + 1)(x - 1) = 0
So, it could be the case that x = 0, x = -1 or x = 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = -x
Add x to both sides to get: 2x = 0
Solve: x = 0
The answer to the target question is x = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

[Max@Math Revolution]

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)

x^3-x = 0
=> x(x^2-1) = 0
=> x(x+1)(x-1) = 0
=> x = 0, x = -1 or x = 1.
Since it does not yield a unique solution, condition 1) is not sufficient.

Condition 2)
x = -x
=> 2x = 0
=> x = 0.
Since it gives a unique solution, condition 2) is sufficient.

Therefore, B is the answer.
Answer: B