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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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14 May 2018, 00:58
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45% (medium)

Question Stats:

71% (02:00) correct 29% (01:46) wrong based on 321 sessions

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GMAT CLUB'S FRESH QUESTION

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

(1) $$x^x < 0$$

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

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

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14 May 2018, 01:19
2
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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11 Jun 2018, 23:11
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.

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

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24 Dec 2018, 02:16
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) $$\frac{|x|}{x}=-1$$

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

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28 Dec 2018, 07:15
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.

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

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28 Dec 2018, 21:21
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) ?   [#permalink] 28 Dec 2018, 21:21
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