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If x ≠ 1, what is the value of (|x| - 1)/(x - 1) ?

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If x ≠ 1, what is the value of (|x| - 1)/(x - 1) ?  [#permalink]

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New post 13 May 2018, 23:58
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E

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  45% (medium)

Question Stats:

67% (01:27) correct 33% (01:21) wrong based on 254 sessions

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Re: If x ≠ 1, what is the value of (|x| - 1)/(x - 1) ?  [#permalink]

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New post 14 May 2018, 00:19
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Bunuel wrote:

GMAT CLUB'S FRESH QUESTION



If x ≠ 1, what is the value of \(\frac{|x| - 1}{x - 1}\)?


(1) \(x^x < 0\)

(2) \(\frac{|x|}{x}=-1\)


The data is sufficient if we get a Unique value for the expression.

Statement 1: \(x^x < 0\)
When x is an odd negative integer, \(x^x < 0\)
Example: x = -3 will satisfy the condition in statement 1. i.e., \((-3)^{(-3)} < 0\) The value of the expression will be 2/(-4) = -1/2
Counter example: x = -5 will also satisfy the condition in staement 1. The value of the expression will be 4/(-6) = -2/3

We are not able to get a unique value for the expression using information about x in statement 1. Statement 1 ALONE is not sufficient.

Statement 2: \(\frac{|x|}{x}=-1\)
We can infer that x is a negative number. We can use the same example and counter example of statement 1 for statement 2 as well to establish that statement 2 is not sufficient.

Combining the two statements:
Example x = -3 satisfies information in the two statements. Value of expression -1/2
Counter example: x = -5 also satisfies information in the two statements. Value of expression -2/3.

Together the statements are not sufficient.
Choice E.
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Re: If x ≠ 1, what is the value of (|x| - 1)/(x - 1) ?  [#permalink]

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New post 11 Jun 2018, 22:11
1
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION



If x ≠ 1, what is the value of \(\frac{|x| - 1}{x - 1}\)?


(1) \(x^x < 0\)

(2) \(\frac{|x|}{x}=-1\)



Statement 1:

\(x^x < 0\)

Gives us that \(x\) is odd & \(x < 0\). Hence \(x\)can be any negative odd value.

Statement 1 alone is Not Sufficient.

Statement 2:

\(\frac{|x|}{x}=-1\)

Gives us that \(x < 0\). Hence \(x\) can take any negative value.

Statement 2 alone is Not Sufficient.

Combining the 2 statements, doesn't give us any new information.

Combining the 2 statements is Not Sufficient.

Answer E.

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GyM
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Re: If x ≠ 1, what is the value of (|x| - 1)/(x - 1) ?  [#permalink]

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New post 24 Dec 2018, 01:16
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Re: If x ≠ 1, what is the value of (|x| - 1)/(x - 1) ?  [#permalink]

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New post 28 Dec 2018, 06:15
Lets get down to statements directly.

1) \(x^x < 0\)
For \(x^x\) to be negative, x needs to satisfy two conditions: a) x needs to be negative and b) x needs to odd so that negative sign of x remains the same.
With these constraints, lets take some values to check sufficiency.

If x=-1. (Note here, x is given not equal to 1, but it can most certainly be -1)
Thus, \(\frac{|x| - 1}{x - 1}\)=0

If x=-3
Thus, \(\frac{|x| - 1}{x - 1}\)=-1/2

Clearly, we cannot arrive at a unique value of the expression. Hence, insufficient

2) \(\frac{|x|}{x}=-1\)

Here, x can take any negative value because the numerator will always be positive (due to mod) and denominator will continue to be negative value. Note here that x doesn't have to be -1 here because the common number in numerator and denominator is essentially cancelling each other and giving us 1 any way.

Now, we can use the same example from statement 1 here (x=-1 and x=-3) and declare that this condition is also insufficient

Combining 1) & 2), we can clearly see that statement 2 is not adding any new information to statement 1 and therefore not changing our result of insufficiency.

Hence, answer is E
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Re: If x ≠ 1, what is the value of (|x| - 1)/(x - 1) ?  [#permalink]

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New post 28 Dec 2018, 20:21
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION



If x ≠ 1, what is the value of \(\frac{|x| - 1}{x - 1}\)?


(1) \(x^x < 0\)

(2) \(\frac{|x|}{x}=-1\)


Analyzing the given expression \(\frac{|x| - 1}{x - 1}\) it can be seen that if x >= 0, Value =1 ( Since |x| = x)

if x < 0 Value of expression cannot be determined unless value of x is known as |x| = - x

St 1 : \(x^x < 0\)

x could be a negative odd integer ex : - 3

or x could be a negative fraction ex : - (1/3)

In either case x is negative and exact value of x is not known

The value of the expression cannot be determined

Not Sufficient

St 2 : \(\frac{|x|}{x}=-1\)

From this it can be concluded that |x| = -x

or x is negative

But value of x is not known, So value of expression cannot be determined

Not Sufficient

Even if we combine both Statements , no additional information is obtained

Choice E
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Re: If x ≠ 1, what is the value of (|x| - 1)/(x - 1) ? &nbs [#permalink] 28 Dec 2018, 20:21
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