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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7584
GMAT 1: 760 Q51 V42 GPA: 3.82
What is the value of x? 1) x^-2x=1 2) x^x=1  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 44% (01:02) correct 56% (01:14) wrong based on 72 sessions

### HideShow timer Statistics [GMAT math practice question]

What is the value of x?

1) $$x^{-2x}=1$$
2) $$x^x=1$$

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
What is the value of x? 1) x^-2x=1 2) x^x=1  [#permalink]

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1
MathRevolution wrote:
[GMAT math practice question]

What is the value of x?

1) $$x^{-2x}=1$$
2) $$x^x=1$$

Hi...

1) $$x^{-2x}=1$$
x can have two values..
1.....$$1^{-2*1}=1^{-2}=\frac{1}{1^2}=1$$
-1.....$$-1^{-2*-1}=-1^{2}=1$$
Insuff

2) $$x^x=1$$
Only possibility is x as 1
suff

B
_________________ V
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1027
Location: India
GPA: 3.64
Re: What is the value of x? 1) x^-2x=1 2) x^x=1  [#permalink]

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S1- $$x^{-2x}$$=1
$$\frac{1}{x^{2x}}$$ = 1
$$x^{2x}$$=1
$$|x^x|$$=1
$$x^x$$ = 1 or -1
Insufficient.

S2 - $$x^x$$=1
Only possible value is x=1.

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7584
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the value of x? 1) x^-2x=1 2) x^x=1  [#permalink]

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=>

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.
We have 1 variable and 0 equation. D is most likely to be the answer.

Condition 1)
Both x =1 and x = -1 satisfy condition 1).
Since the solution are not unique, this condition is not sufficient.

Condition 2)
Only x = 1 satisfies condition 2).
This is sufficient.
Note. 00 = 1 is not in the scope of GMAT exam.

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 con 1) and con 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. D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E.

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

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_________________ Re: What is the value of x? 1) x^-2x=1 2) x^x=1   [#permalink] 27 Jun 2019, 05:23
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