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

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Math Revolution GMAT Instructor
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What is the value of x? 1) x^-2x=1 2) x^x=1  [#permalink]

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New post 20 Oct 2017, 01:09
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (00:35) correct 44% (00:44) wrong based on 81 sessions

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[GMAT math practice question]

What is the value of x?

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

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

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New post 20 Oct 2017, 01:30
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.....\(-1^{-2*-1}=-1^{2}=1\)
different answers possible
Insuff

2) \(x^x=1\)
Only possibility is x as 1
suff

B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 20 Oct 2017, 10:25
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.

Answer B

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

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New post 22 Oct 2017, 21:17
=>

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.

Therefore, B is the answer.

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.


Answer: B
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Re: What is the value of x? 1) x^-2x=1 2) x^x=1 &nbs [#permalink] 22 Oct 2017, 21:17
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