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What is the value of x? 1) x^-4x=1 2) x^-x=1

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What is the value of x? 1) x^-4x=1 2) x^-x=1 [#permalink]

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New post 29 Sep 2017, 01:26
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

46% (00:39) correct 54% (00:41) wrong based on 28 sessions

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[GMAT math practice question]

What is the value of x?

1) \(x^{-4x}\)=1
2) \(x^{-x}\)=1
[Reveal] Spoiler: OA

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What is the value of x? 1) x^-4x=1 2) x^-x=1 [#permalink]

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New post 29 Sep 2017, 04:56
MathRevolution wrote:
[GMAT math practice question]

What is the value of x?

1) \(x^{-4x}\)=1
2) \(x^{-x}\)=1


Statement 1: there are two possible values of \(x\), \(x=1\) or \(x=-1\). Hence insufficient

Statement 2: implies that \(x^{-x}=1\), only one possible solution \(x=1\). Hence sufficient

Option B

Last edited by niks18 on 01 Oct 2017, 20:13, edited 1 time in total.

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Re: What is the value of x? 1) x^-4x=1 2) x^-x=1 [#permalink]

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New post 01 Oct 2017, 18:19
=>
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.

Condition 1)
We have 2 possible values, which are x = 1 and x = -1.
This is not sufficient.

Condition 2)
The only possible value is x = 1.

Therefore, the answer is B unlike our expectation.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Answer: B
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Re: What is the value of x? 1) x^-4x=1 2) x^-x=1   [#permalink] 01 Oct 2017, 18:19
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