Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 15 Jul 2019, 11:18

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56226
If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?  [#permalink]

### Show Tags

14 May 2018, 01:08
2
13
00:00

Difficulty:

95% (hard)

Question Stats:

44% (02:36) correct 56% (02:54) wrong based on 196 sessions

### HideShow timer Statistics

GMAT CLUB'S FRESH QUESTION

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

(1) $$\sqrt{x^6} > x^3$$

(2) $$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$

_________________
Manager
Joined: 24 Nov 2017
Posts: 60
Location: India
GMAT 1: 720 Q51 V36
Re: If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?  [#permalink]

### Show Tags

14 May 2018, 01:36
2
2
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION

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

(1) $$\sqrt{x^6} > x^3$$

(2) $$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$

The data is sufficient if we get a unique value for the expression $$\frac{-|x| - 1}{x - 1}$$
A quick info about this expression. If x is negative then the expression will have a unique value, which is 1.
If x is 0, it will have a unique value, which is 1.
If x is positive it will have multiple values. For instance, if x = 2, the value of the expression is -3. If x = 3, the value of the expression -2.

So, at some level if we can establish that x is not positive, we will have a unique value. Else we will not have a unique value.

Statement 1: $$\sqrt{x^6} > x^3$$
$$\sqrt{x^6}$$ is non negative for real x and will be |x^3|.
For instance $$\sqrt{2^6}$$ = 8 and $$\sqrt{{(-2)^6}$$ will also be 8.
But 2^3 will be 8 and (-2)^3 will be -8.
So, if we know that $$\sqrt{x^6} > x^3$$, we can infer that x is negative.

If x is negative, the value of $$\frac{-|x| - 1}{x - 1}$$ will be 1. Take any negative x and check it. Negative integer, negative non integer. It will work for all values.

So, statement 1 ALONE is sufficient.

Statement 2:$$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$
We can rewrite the expression as |x| + 2x + 4|x| + 8x = -16
5|x| + 10x = -16.
The sum of the expression is -16, which is negative.
5|x| cannot be negative. So, 10x has to be negative if the sum is -16 => x has to be negative.

If x is negative, the expression $$\frac{-|x| - 1}{x - 1}$$ has a unique value which is 1.

Statement 2 ALONE is sufficient.

Each statement is INDEPENDENTLY sufficient.
Choice D.
_________________
An IIM C Alumnus - Class of '94
GMAT Tutor at Wizako GMAT Classes & Online Courses
##### General Discussion
BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 512
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?  [#permalink]

### Show Tags

14 May 2018, 01:55
$$\frac{-|x| - 1}{x - 1}$$

Looking at the question, we can identify that any positive number will yield different values for the expression(such as 2, 4, 6). But any non-positive number will always yield the answer 1(such as 0, -0.5, -1, -4 ). Hence if we are able to find out that x is non-positive, we can sufficiently get the answer

Statement 1: -

$$\sqrt{x^6} > x^3$$

Therefore $$|x^3| > x^3$$

This tells us that x is negative. Hence it is SUFFICIENT

Statement 1: -

$$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$

Taking LCM, we can reduce the equation to

$$\frac{|x|+2x+4|x|+8x}{16} = -1$$

5|x| +10x + 16 =0

case 1 : - Now if x is positive, then the equation above will never be 0

case 2 : - Now if x is negative, then the equation above will be 0 for a value of x

Hence, this option is also SUFFICIENT

_________________
SVP
Joined: 26 Mar 2013
Posts: 2282
Re: If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?  [#permalink]

### Show Tags

15 May 2018, 15:32
pikolo2510 wrote:
$$\frac{-|x| - 1}{x - 1}$$

Looking at the question, we can identify that any positive number will yield different values for the expression(such as 2, 4, 6). But any non-positive number will always yield the answer 1(such as 0, -0.5, -1, -4 ). Hence if we are able to find out that x is non-positive, we can sufficiently get the answer

Statement 1: -

$$\sqrt{x^6} > x^3$$

Therefore $$|x^3| > x^3$$

This tells us that x is negative. Hence it is SUFFICIENT

Statement 1: -

$$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$

Taking LCM, we can reduce the equation to

$$\frac{|x|+2x+4|x|+[highlight]8[}{highlight]/16} = -1$$

5|x| +2x + 24 =0

case 1 : - Now if x is positive, then the equation above will never be 0

case 2 : - Now if x is negative, then the equation above will be 0 for a value of x

Hence, this option is also SUFFICIENT

Hi, You missed to multiply 8 by x. This will change the shape of the equation to be

5|x| +10x =-16
BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 512
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
Re: If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?  [#permalink]

### Show Tags

15 May 2018, 21:00
Mo2men wrote:
pikolo2510 wrote:
$$\frac{-|x| - 1}{x - 1}$$

Looking at the question, we can identify that any positive number will yield different values for the expression(such as 2, 4, 6). But any non-positive number will always yield the answer 1(such as 0, -0.5, -1, -4 ). Hence if we are able to find out that x is non-positive, we can sufficiently get the answer

Statement 1: -

$$\sqrt{x^6} > x^3$$

Therefore $$|x^3| > x^3$$

This tells us that x is negative. Hence it is SUFFICIENT

Statement 1: -

$$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$

Taking LCM, we can reduce the equation to

$$\frac{|x|+2x+4|x|+[highlight]8[}{highlight]/16} = -1$$

5|x| +2x + 24 =0

case 1 : - Now if x is positive, then the equation above will never be 0

case 2 : - Now if x is negative, then the equation above will be 0 for a value of x

Hence, this option is also SUFFICIENT

Hi, You missed to multiply 8 by x. This will change the shape of the equation to be

5|x| +10x =-16

Thanks for pointing that typo out. Edited my original solution
_________________
Retired Moderator
Joined: 27 Oct 2017
Posts: 1229
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?  [#permalink]

### Show Tags

23 May 2018, 11:23
What is the value of $$\frac{-|x| - 1}{x - 1}$$
if x<0, = $$\frac{x-1}{x-1}$$ = 1
if x>0, $$\frac{-x-1}{x-1}$$, the value depends on value of x

Statement 1) $$\sqrt{x^6} > x^3$$
it is clear that x is negative, because if x is non negative, $$\sqrt{x^6} = x^3$$
So, x is negative and $$\frac{x-1}{x-1}$$ = 1
SUFFICIENT

Statement 2) $$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$
Since RHS is negative, We can straight away say that x is NEGATIVE, as all terms in LHS are in addition, we cant have the additions of positive terms = negative. (There is no need to solve the equation)
So x is negative and and $$\frac{x-1}{x-1}$$ = 1
SUFFICIENT

Bunuel wrote:

GMAT CLUB'S FRESH QUESTION

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

(1) $$\sqrt{x^6} > x^3$$

(2) $$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 56226
Re: If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?  [#permalink]

### Show Tags

24 Dec 2018, 02:19
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION

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

(1) $$\sqrt{x^6} > x^3$$

(2) $$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$

_________________
Manager
Joined: 24 Nov 2018
Posts: 109
Location: India
GPA: 3.27
WE: General Management (Retail Banking)
Re: If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?  [#permalink]

### Show Tags

25 Dec 2018, 22:08
Bunuel wrote:

GMAT CLUB'S FRESH QUESTION

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

(1) $$\sqrt{x^6} > x^3$$

(2) $$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$

Statement 1) $$\sqrt{x^6} > x^3$$ implies x is negative because square root is always positive so, square root of x^6 is positive and x^3 is negative. Only in the case of x being negative, this statement holds true. So, if x is negative. -|x|=x as |x| will be -x and -(-x)=x. The expression reduces to $$\frac{x - 1}{x - 1}$$=1. Sufficient.

Statement 2) $$\frac{|x|}{16} + \frac{x}{8} + \frac{|x|}{4} + \frac{x}{2} = -1$$. Simplifying, we get $$\frac{5*|x|}{16} + \frac{5*x}{8}= -1$$ or $$\frac{5*|x|}{16} + \frac{10*x}{16}= -1$$. Further simplyfying, $$5*|x| + 10*x= -16$$. Now, |x| will always be positive, so, x has to be negative to equate to -16 on RHS. Also, multiple of x is higher than of multiple of |X|, so, x has to be negative in order to total to -16. If x is positive, the expression won't hold true. Following the logic in Statement 1, if x is negative, the expression in the problem reduces to $$\frac{x - 1}{x - 1}$$=1. Sufficient.

Hence, D is the correct answer.
_________________
Kudos encourage discussions. Share it to amplify collective education!
Re: If x ≠ 1, what is the value of (-|x| - 1)/(x - 1) ?   [#permalink] 25 Dec 2018, 22:08
Display posts from previous: Sort by