GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Jan 2020, 21:40

### 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 is an integer, is |x|>1.

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Jan 2010
Posts: 233
If x is an integer, is |x|>1.  [#permalink]

### Show Tags

27 Apr 2012, 16:14
8
00:00

Difficulty:

85% (hard)

Question Stats:

55% (02:20) correct 45% (02:19) wrong based on 121 sessions

### HideShow timer Statistics

If x is an integer, is |x|>1.

(1) (1-2x)(1+x) < 0
(2) (1-x)(1+2x) < 0

Can somebody please explain this question?

Thanks
Vikram
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

27 Apr 2012, 22:22
3
1
If x is an integer, is |x|>1.

(1) (1-2x)(1+x) < 0
(2) (1-x)(1+2x) < 0

Can somebody please explain this question?

Thanks
Vikram

This post might help to get the ranges for (1) and (2) - "How to solve quadratic inequalities - Graphic approach": x2-4x-94661.html#p731476

If x is an integer, is |x| > 1?

First of all: is $$|x| > 1$$ means is $$x<-1$$ (-2, -3, -4, ...) or $$x>1$$ (2, 3, 4, ...), so for YES answer $$x$$ can be any integer but -1, 0, and 1.

(1) (1 - 2x)(1 + x) < 0 --> rewrite as $$(2x-1)(x+1)>0$$ (so that the coefficient of x^2 to be positive after expanding): roots are $$x=-1$$ and $$x=\frac{1}{2}$$ --> "$$>$$" sign means that the given inequality holds true for: $$x<-1$$ and $$x>\frac{1}{2}$$. $$x$$ could still equal to 1, so not sufficient.

(2) (1 - x)(1 + 2x) < 0 --> rewrite as $$(x-1)(2x+1)>0$$: roots are $$x=-\frac{1}{2}$$ and $$x=1$$ --> "$$>$$" sign means that the given inequality holds true for: $$x<-\frac{1}{2}$$ and $$x>1$$. $$x$$ could still equal to -1, so not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is $$x<-1$$ and $$x>1$$. Sufficient.

This question is also discussed here: m14-72785.html

Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
_________________
Manager
Joined: 26 Dec 2011
Posts: 89
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

10 May 2012, 06:48
roots are x=-1 and x=1/2 and --> ">" sign means that the given inequality holds true for: x<-1 and x>1/2 ... can you please help me with this concept and what will happen if sign was "<"..further, will it be right in stating that when there is a positive sign, x is greater than the positive root and x is less than the negative root?
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

10 May 2012, 06:49
pavanpuneet wrote:
roots are x=-1 and x=1/2 and --> ">" sign means that the given inequality holds true for: x<-1 and x>1/2 ... can you please help me with this concept and what will happen if sign was "<"..further, will it be right in stating that when there is a positive sign, x is greater than the positive root and x is less than the negative root?

Explained here:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
_________________
Manager
Joined: 13 May 2010
Posts: 101
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

19 Jul 2012, 19:23
Bunuel wrote:
If x is an integer, is |x|>1.

(1) (1-2x)(1+x) < 0
(2) (1-x)(1+2x) < 0

Can somebody please explain this question?

Thanks
Vikram

This post might help to get the ranges for (1) and (2) - "How to solve quadratic inequalities - Graphic approach": x2-4x-94661.html#p731476

If x is an integer, is |x| > 1?

First of all: is $$|x| > 1$$ means is $$x<-1$$ (-2, -3, -4, ...) or $$x>1$$ (2, 3, 4, ...), so for YES answer $$x$$ can be any integer but -1, 0, and 1.

(1) (1 - 2x)(1 + x) < 0 --> rewrite as $$(2x-1)(x+1)>0$$ (so that the coefficient of x^2 to be positive after expanding): roots are $$x=-1$$ and $$x=\frac{1}{2}$$ --> "$$>$$" sign means that the given inequality holds true for: $$x<-1$$ and $$x>\frac{1}{2}$$. $$x$$ could still equal to 1, so not sufficient.

(2) (1 - x)(1 + 2x) < 0 --> rewrite as $$(x-1)(2x+1)>0$$: roots are $$x=-\frac{1}{2}$$ and $$x=1$$ --> "$$>$$" sign means that the given inequality holds true for: $$x<-\frac{1}{2}$$ and $$x>1$$. $$x$$ could still equal to -1, so not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is $$x<-1$$ and $$x>1$$. Sufficient.

This question is also discussed here: m14-72785.html

Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

I have a question regarding the above solution let's say in statement 1, when you solve the inequality why do you say that x<-1 AND x >1/2

why is this an AND condition ....why not OR? If this were a quadratic equation x (can be) = 1/2 OR -1 OR both
For inequality why is the same thing an AND as opposed to OR?
Intern
Joined: 12 Dec 2012
Posts: 28
GMAT 2: 660 Q48 V33
GMAT 3: 740 Q49 V41
GPA: 3.74
Solving compounded inequalities - any efficient approach?  [#permalink]

### Show Tags

23 Oct 2013, 19:58
If x is an integer, is |x|>1?

(1) (1−2x)(1+x)<0

(2) (1−x)(1+2x)<0

Hi all - I tried this problem on a GMAT club test and I didn't really understand the method. Any quick approaches to finding the solution to each inequality? Is there any quick method to figure out the range of values of x for which statement 1 and 2 will be accurate?

Help appreciated! I'd like to know the quickest, most efficient way to approach such problems!

Cheers
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: Solving compounded inequalities - any efficient approach?  [#permalink]

### Show Tags

24 Oct 2013, 01:05
sidvish wrote:
If x is an integer, is |x|>1?

(1) (1−2x)(1+x)<0

(2) (1−x)(1+2x)<0

Hi all - I tried this problem on a GMAT club test and I didn't really understand the method. Any quick approaches to finding the solution to each inequality? Is there any quick method to figure out the range of values of x for which statement 1 and 2 will be accurate?

Help appreciated! I'd like to know the quickest, most efficient way to approach such problems!

Cheers

Merging similar topics. Please refer to the solution above.

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 14003
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

29 Nov 2019, 10:37
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x is an integer, is |x|>1.   [#permalink] 29 Nov 2019, 10:37
Display posts from previous: Sort by
To analyze the given text passage, I will first describe its content structure and then provide the required analysis.

The text passage appears to be a GMAT question, specifically a Data Sufficiency problem. It presents a question about the absolute value of an integer and provides two statements with inequalities. The goal is to determine if the statements are sufficient to answer the question.

Here is the analysis in the requested format:
single_question_with_answer

the passage contains a single mathematical question: "if x is an integer, is |x| > 1?" it also provides two statements that can be used to determine the answer to this question. the solution provided in the passage explains how to use the given statements to find the answer, indicating that the question is answered using the information provided.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Jan 2020, 21:40

### 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 is an integer, is |x|>1.

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Jan 2010
Posts: 233
If x is an integer, is |x|>1.  [#permalink]

### Show Tags

27 Apr 2012, 16:14
8
00:00

Difficulty:

85% (hard)

Question Stats:

55% (02:20) correct 45% (02:19) wrong based on 121 sessions

### HideShow timer Statistics

If x is an integer, is |x|>1.

(1) (1-2x)(1+x) < 0
(2) (1-x)(1+2x) < 0

Can somebody please explain this question?

Thanks
Vikram
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

27 Apr 2012, 22:22
3
1
If x is an integer, is |x|>1.

(1) (1-2x)(1+x) < 0
(2) (1-x)(1+2x) < 0

Can somebody please explain this question?

Thanks
Vikram

This post might help to get the ranges for (1) and (2) - "How to solve quadratic inequalities - Graphic approach": x2-4x-94661.html#p731476

If x is an integer, is |x| > 1?

First of all: is $$|x| > 1$$ means is $$x<-1$$ (-2, -3, -4, ...) or $$x>1$$ (2, 3, 4, ...), so for YES answer $$x$$ can be any integer but -1, 0, and 1.

(1) (1 - 2x)(1 + x) < 0 --> rewrite as $$(2x-1)(x+1)>0$$ (so that the coefficient of x^2 to be positive after expanding): roots are $$x=-1$$ and $$x=\frac{1}{2}$$ --> "$$>$$" sign means that the given inequality holds true for: $$x<-1$$ and $$x>\frac{1}{2}$$. $$x$$ could still equal to 1, so not sufficient.

(2) (1 - x)(1 + 2x) < 0 --> rewrite as $$(x-1)(2x+1)>0$$: roots are $$x=-\frac{1}{2}$$ and $$x=1$$ --> "$$>$$" sign means that the given inequality holds true for: $$x<-\frac{1}{2}$$ and $$x>1$$. $$x$$ could still equal to -1, so not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is $$x<-1$$ and $$x>1$$. Sufficient.

This question is also discussed here: m14-72785.html

Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
_________________
Manager
Joined: 26 Dec 2011
Posts: 89
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

10 May 2012, 06:48
roots are x=-1 and x=1/2 and --> ">" sign means that the given inequality holds true for: x<-1 and x>1/2 ... can you please help me with this concept and what will happen if sign was "<"..further, will it be right in stating that when there is a positive sign, x is greater than the positive root and x is less than the negative root?
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

10 May 2012, 06:49
pavanpuneet wrote:
roots are x=-1 and x=1/2 and --> ">" sign means that the given inequality holds true for: x<-1 and x>1/2 ... can you please help me with this concept and what will happen if sign was "<"..further, will it be right in stating that when there is a positive sign, x is greater than the positive root and x is less than the negative root?

Explained here:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
_________________
Manager
Joined: 13 May 2010
Posts: 101
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

19 Jul 2012, 19:23
Bunuel wrote:
If x is an integer, is |x|>1.

(1) (1-2x)(1+x) < 0
(2) (1-x)(1+2x) < 0

Can somebody please explain this question?

Thanks
Vikram

This post might help to get the ranges for (1) and (2) - "How to solve quadratic inequalities - Graphic approach": x2-4x-94661.html#p731476

If x is an integer, is |x| > 1?

First of all: is $$|x| > 1$$ means is $$x<-1$$ (-2, -3, -4, ...) or $$x>1$$ (2, 3, 4, ...), so for YES answer $$x$$ can be any integer but -1, 0, and 1.

(1) (1 - 2x)(1 + x) < 0 --> rewrite as $$(2x-1)(x+1)>0$$ (so that the coefficient of x^2 to be positive after expanding): roots are $$x=-1$$ and $$x=\frac{1}{2}$$ --> "$$>$$" sign means that the given inequality holds true for: $$x<-1$$ and $$x>\frac{1}{2}$$. $$x$$ could still equal to 1, so not sufficient.

(2) (1 - x)(1 + 2x) < 0 --> rewrite as $$(x-1)(2x+1)>0$$: roots are $$x=-\frac{1}{2}$$ and $$x=1$$ --> "$$>$$" sign means that the given inequality holds true for: $$x<-\frac{1}{2}$$ and $$x>1$$. $$x$$ could still equal to -1, so not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) is $$x<-1$$ and $$x>1$$. Sufficient.

This question is also discussed here: m14-72785.html

Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

I have a question regarding the above solution let's say in statement 1, when you solve the inequality why do you say that x<-1 AND x >1/2

why is this an AND condition ....why not OR? If this were a quadratic equation x (can be) = 1/2 OR -1 OR both
For inequality why is the same thing an AND as opposed to OR?
Intern
Joined: 12 Dec 2012
Posts: 28
GMAT 2: 660 Q48 V33
GMAT 3: 740 Q49 V41
GPA: 3.74
Solving compounded inequalities - any efficient approach?  [#permalink]

### Show Tags

23 Oct 2013, 19:58
If x is an integer, is |x|>1?

(1) (1−2x)(1+x)<0

(2) (1−x)(1+2x)<0

Hi all - I tried this problem on a GMAT club test and I didn't really understand the method. Any quick approaches to finding the solution to each inequality? Is there any quick method to figure out the range of values of x for which statement 1 and 2 will be accurate?

Help appreciated! I'd like to know the quickest, most efficient way to approach such problems!

Cheers
Math Expert
Joined: 02 Sep 2009
Posts: 60627
Re: Solving compounded inequalities - any efficient approach?  [#permalink]

### Show Tags

24 Oct 2013, 01:05
sidvish wrote:
If x is an integer, is |x|>1?

(1) (1−2x)(1+x)<0

(2) (1−x)(1+2x)<0

Hi all - I tried this problem on a GMAT club test and I didn't really understand the method. Any quick approaches to finding the solution to each inequality? Is there any quick method to figure out the range of values of x for which statement 1 and 2 will be accurate?

Help appreciated! I'd like to know the quickest, most efficient way to approach such problems!

Cheers

Merging similar topics. Please refer to the solution above.

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 14003
Re: If x is an integer, is |x|>1.  [#permalink]

### Show Tags

29 Nov 2019, 10:37
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x is an integer, is |x|>1.   [#permalink] 29 Nov 2019, 10:37
Display posts from previous: Sort by
user
To analyze the given text passage, I will first describe its content structure and then provide the required analysis.

The text passage appears to be a GMAT question, specifically a Data Sufficiency problem. It presents a question about the absolute value of an integer and provides two statements with inequalities. The goal is to determine if the statements are sufficient to answer the question.

Here is the analysis in the requested format:

TYPE: SINGLE_QUESTION_WITH_ANSWER

The passage contains a single mathematical question: "If x is an integer, is |x| > 1?" It also provides two statements that can be used to determine the answer to this question. The solution provided in the passage explains how to use the given statements to find the answer, indicating that the question is answered using the information provided.