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Intern
Status: MBA Student
Joined: 20 Nov 2017
Posts: 30
Location: India
Concentration: Strategy, Marketing
GPA: 3.9
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11 Jul 2018, 05:44
2
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Difficulty:

35% (medium)

Question Stats:

62% (01:14) correct 38% (00:58) wrong based on 55 sessions

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x=?

1. $$x^{4x}=1$$
2. $$x^{-x}=-1$$
Intern
Joined: 08 Jul 2018
Posts: 39

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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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Joined: 19 Nov 2017
Posts: 186
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
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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

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Joined: 02 Aug 2009
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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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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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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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