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x=?

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x=?

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[Math Revolution GMAT math practice question]

x=?

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

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

x=?

1) x^3+x^2+x=0
2) x=-2x
\[? = x\]
\[\left( 1 \right)\,\,\,x\left( {{x^2} + x + 1} \right) = 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \begin{gathered}
x = 0 \hfill \\
\,\,\,{\text{OR}} \hfill \\
{x^2} + x + 1 = 0 \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\mathop {\, \Rightarrow }\limits^{\left( * \right)} \,\,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\]
\[\left( * \right)\,\,\,\,{x^2} + x + 1 = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\Delta = {\left( 1 \right)^2} - 4 \cdot 1 \cdot 1 < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{x^2} + x + 1 > 0\,\,\,\,{\text{for}}\,\,{\text{all}}\,\,\,\,x\,\,\,\,\,\,\,\,\,\,\,\]

\[\left( 2 \right)\,\,\,x = - 2x\,\,\,\,\, \Rightarrow \,\,\,\,3x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\]

The right answer is therefore _(D)____ .

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

Regards,
Fabio.

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English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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

x=?

1) x^3+x^2+x=0
2) x=-2x
We have to get the value of x.

Let's take each statement one by one.

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

There can be three possibilities.

1. x = 0.
2. x is positive. This is not possible since the sum of three positive numbers cannot be 0. Rules out.
3. x can be negative.

Note that for x < 0, the value of x^2 is positive and the value fo x^3 + x is negative; thus, to make the sum of x^3 + x equal to x^2, we must have |x^3 + x| = x^2.

3a. x ≤ -1. This is not possible since in this scenario, |x^3| > x^2. Rules out.
3b. 0 < x < -1. This is not possible since in this scenario, |x| > x^2. Rules out.

Thus, x = 0. Sufficient.

2) x = -2x

=> 3x = 0 => x = 0. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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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 of the conditions on their own first.

Condition 1)
x^3+x^2+x=0
=> x(x^2+x+1)=0
=> x = 0 since x^2+x+1 ≠ 0
Condition 1) is sufficient.

Condition 2)
x = -2x
=> 3x = 0
=> x = 0
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

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.

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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

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