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x=?  [#permalink]

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New post 11 Jul 2018, 05:44
2
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A
B
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D
E

Difficulty:

  35% (medium)

Question Stats:

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x=?

1. \(x^{4x}=1\)
2. \(x^{-x}=-1\)
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Re: x=?  [#permalink]

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New post 11 Jul 2018, 05:52
1
Karthik200 wrote:
x=?

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


Hi,

1. x can be both 1 and -1. NS.
2. x can only be -1. Hence B
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Re: x=?  [#permalink]

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New post 11 Jul 2018, 07:11
Karthik200 wrote:
x=?

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


Statement 1

\(x^{4x}=1\).
x could be 1 or -1 or 0
INSUFFICIENT

Statement 2

\(x^{-x}=-1\)
x can only be -1
\((-1)^1 = -1\)
SUFFICIENT

Answer is B.
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Re: x=?  [#permalink]

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New post 11 Jul 2018, 07:51
1
x=?

1. \(x^{4x}=1\)
How can this happen...
a) the power 4x=0 or x=0 but then it becomes 0^0
b) the exponent x is |1|, so when x=1..1^(4*1)=1^1=1
and when x=-1.....\(-1^{4*-1}=\frac{1}{-1^4}=1\)
Insufficient

2. \(x^{-x}=-1\)
Again as the cases above ..
0 not possible, lets check for 1 and -1
\(1^{-1}=1/1=1\neq{-1}\)..
\((-1)^{-1(-1)}=(-1)^1=-1\)..
So x=-1
Sufficient

B
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Re: x=?  [#permalink]

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New post 11 Jul 2018, 08:02
Karthik200 wrote:
x=?

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


S1 - \(x^{4x}=1\)
can be possible if x=0, 1 or -1.
Plugging in these values will give result 1.
Insufficient.

S2 - \(x^{-x}=-1\)
This statement rules out the possibilities of 0,1.
Hence x=-1. Sufficient.
Ans. B
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Re: x=?  [#permalink]

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New post 11 Jul 2018, 09:40
This is a value question & NOT a yes/no question

Statement 1 satisfies multiple values ( e.g. 1 & -1) hence we cannot have a definite value of x

Statement 2 gives a single value of x, i.e. -1.

Option B is the correct answer!
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Re: x=?   [#permalink] 11 Jul 2018, 09:40
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