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If x ≠ 0, what is the value of x?

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Math Expert
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If x ≠ 0, what is the value of x?  [#permalink]

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10 Oct 2017, 01:06
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Difficulty:

55% (hard)

Question Stats:

60% (01:39) correct 40% (01:36) wrong based on 186 sessions

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Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) $$(\frac{x}{2})^x = 1$$

(2) $$(|x|)^x = 4$$

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Re: If x ≠ 0, what is the value of x?  [#permalink]

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08 Oct 2019, 04:35
1
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) $$(\frac{x}{2})^x = 1$$

(2) $$(|x|)^x = 4$$

Asked: If x ≠ 0, what is the value of x?

(1) $$(\frac{x}{2})^x = 1$$
x = 2 or -2
NOT SUFFICIENT

(2) $$(|x|)^x = 4$$
x = 2
SUFFICIENT

IMO B
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Re: If x ≠ 0, what is the value of x?  [#permalink]

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10 Oct 2017, 02:37
(1) (x/2)^x=1
Testing differenet cases we get that x=2 or -2 so we cannot define concrete value.
x=2
(2/2)^2=1

x=-2

(-2/2)^-2= (-1)^-2=1/(-1)^2=1

Insufficient

(2) After testing cases I got that only x=2 satisfies the equation (|x|)^x=4
P.S. maybe there is something more.

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If x ≠ 0, what is the value of x?  [#permalink]

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11 Oct 2017, 09:58
Alexey1989x wrote:
(1) (x/2)^x=1
Testing differenet cases we get that x=2 or -2 so we cannot define concrete value.
x=2
(2/2)^2=1

x=-2

(-2/2)^-2= (-1)^-2=1/(-1)^2=1

Insufficient

(2) After testing cases I got that only x=2 satisfies the equation (|x|)^x=4
P.S. maybe there is something more.

Same here but am wondering if there is some kind of trickery involved here :D
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Re: If x ≠ 0, what is the value of x?  [#permalink]

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11 Oct 2017, 10:11
I believe that Alexey1989x is correct on this one. I also came up with B with statement 1 capabile of being x = -2 or 2. Here is my breakdown for using x = -2

(-2/2)^-2 = ((-2)^-2)/ (2^-2) = (1/-2^2)/(1/2^2) = 1/4 / 1/4 = 1

Any other thoughts are welcome!
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Re: If x ≠ 0, what is the value of x?  [#permalink]

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11 Oct 2017, 10:32
If x ≠ 0, what is the value of x?

(1) $$(\frac{x}{2})^x = 1$$
=> if x = 2 => $$(\frac{x}{2})^x$$ = $$(\frac{2}{2})^2 = 1$$ => Satisfy the given equation
or
=> if x = -2 => $$(\frac{x}{2})^x = (\frac{-2}{2})^{-2} = (\frac{1}{(-1)})^2 = 1$$ => Satisfy the given equation

So possible values of x = 2 and -2
Insufficient

(2) $$(|x|)^x = 4$$

if x = 2 => $$(|x|)^x = (|2|)^2 = 4$$ => Satisfy the given equation
or
if x = -2 => $$(|x|)^x = (|-2|)^{-2} = (2)^{-2} = (\frac{1}{2})^2 = \frac{1}{4}$$ => Does not satisfy the given equation

So only possible value of x = 2
Sufficient

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If x ≠ 0, what is the value of x?  [#permalink]

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11 Oct 2017, 10:45
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) $$(\frac{x}{2})^x = 1$$

(2) $$(|x|)^x = 4$$

Substitution method has already been explained and in this problem numbers can be easily substituted because visually you can identify the number which will work when substituted.

Algebraic method could be -

Statement 1: RHS is an integer $$1$$ so LHS has to be integer. This implies $$x$$ is divisible by $$2$$ i.e. even, hence can take both positive and negative values when $$x$$th root is calculated

So raising both sides of the equation to power $$\frac{1}{x}$$, we get

$$\frac{x}{2}=1^\frac{1}{x}$$. Now $$1$$ raised to any power will be $$1$$ but as $$x$$ is even so in this case it will be

$$\frac{x}{2}= ±1$$, so $$x=±2$$

As we get two values of $$x$$, hence this statement is Insufficient

Statement 2: LHS is of the form $$x^x$$ or $$(-x)^x$$, (if $$x<0$$)

RHS $$4= 2^2$$ and there is no other possibility where both base and exponent will be equal ($$2^{-2}=\frac{1}{4}$$)

Hence $$x=2$$. Sufficient

Option B
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Re: If x ≠ 0, what is the value of x?  [#permalink]

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24 Dec 2018, 02:56
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) $$(\frac{x}{2})^x = 1$$

(2) $$(|x|)^x = 4$$

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Re: If x ≠ 0, what is the value of x?  [#permalink]

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26 Dec 2018, 00:05
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) $$(\frac{x}{2})^x = 1$$

(2) $$(|x|)^x = 4$$

Statement 1) x can 2 or -2. Insufficient.

Statement 2) x has to be 2. Sufficient.

Hence, Option B.
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Re: If x ≠ 0, what is the value of x?   [#permalink] 26 Dec 2018, 00:05
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