Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Is x < 0?

1) |x|=-x
2) |x|>x

\[x\,\,\mathop < \limits^? \,\,0\]

\[\left( 1 \right)\,\,\,\left| x \right| = - x\,\,\,\,\, \Leftrightarrow \,\,\,\,x \leqslant 0\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,x = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\
\,{\text{Take}}\,\,x = - 1\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,\,x < \left| x \right|\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,x < 0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}{\text{.}}\,\,\,\,\]
\[\left( * \right)\,\,x \geqslant 0\,\,\,\, \Rightarrow \,\,\,x = \left| x \right|\]


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

=>

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 of the conditions on their own first.

Condition 1)
|x| = -x
=> x ≤ 0
In inequality questions, the law "Question is King" tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient.
Since the solution set "x<0" of the question doesn't include the solution set "x ≤ 0" of the condition 1), condition 1) is not sufficient.

Condition 2)
|x|>x
=> x < 0
Since condition 2) is equivalent to the question, condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.