Data Sufficiency

[Math Revolution GMAT math practice question]

x=?

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

Max@Math Revolution wrote:[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.

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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