It is currently 17 Oct 2017, 05:03

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x is an integer, what is the value of x?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

4 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 07 Nov 2009
Posts: 305

Kudos [?]: 685 [4], given: 20

If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 01 Feb 2012, 22:58
4
This post received
KUDOS
26
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:48) correct 67% (01:38) wrong based on 778 sessions

HideShow timer Statistics

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2
(2) |x^2 - |x|| = 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Dec 2012, 02:53, edited 1 time in total.
Edited the question.

Kudos [?]: 685 [4], given: 20

3 KUDOS received
Manager
Manager
avatar
Joined: 03 Oct 2009
Posts: 60

Kudos [?]: 148 [3], given: 8

Re: value of x [#permalink]

Show Tags

New post 01 Feb 2012, 23:29
3
This post received
KUDOS
2
This post was
BOOKMARKED
If x is an integer, what is the value of x?
1) |x - |x^2|| = 2
x^2 is always positive. so |x^2| = x^2

x - x^2 is negative since X^2 > x for an integer

-(x - x^2) = 2
-x + x^2 = 2
x^2 -x - 2 = 0
x^2 -2x +x - 2 = 0
(x-2) (x+1)
x = 2 or x = -1 , two values , not sufficient.

2) |x2 - |x|| = 2
x^2 - |x| is positive since X^2 > x for an integer

|x| can be positive or negative. so two scenarios.

x^2 -x = 2
x^2 -x - 2 = 0
(x-2)(x+1) = 0

or

x^2 + x = 2
x^2 + x - 2 = 0
(x+2) (x-1) = 0

Multiple values so not sufficient.

(1) + (2) , still not sufficient.

Kudos [?]: 148 [3], given: 8

2 KUDOS received
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1286

Kudos [?]: 281 [2], given: 10

Re: value of x [#permalink]

Show Tags

New post 02 Feb 2012, 01:39
2
This post received
KUDOS
a.
squaring both sides we get
x^2 + x^4 - 2x* x^2 = 4
meaning, x^2 (x-1)^2 = 4
thus x = 2 | -1 not sufficient.

b same process and we get x = 2| -2
not sufficient.

a+b gives x = 2.

thus C it is.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!


Last edited by amit2k9 on 03 Feb 2012, 02:03, edited 1 time in total.

Kudos [?]: 281 [2], given: 10

4 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 19 Apr 2011
Posts: 275

Kudos [?]: 376 [4], given: 51

Schools: Booth,NUS,St.Gallon
Re: value of x [#permalink]

Show Tags

New post 02 Feb 2012, 04:07
4
This post received
KUDOS
1
This post was
BOOKMARKED
If x is an integer, what is the value of x?
1) |x - |x2|| = 2
2) |x2 - |x|| = 2

Hi Rohit,these type of questions are extremely easy.they just seem to be intimidating but they are not .
You just need to know one concept
[x]= x if x is positive
[x]=-x if x is negative.

Now take 1) |x - |x2|| = 2

|x2| is always positive. |x - |x2|| is negative since x^2>x

x^2-x=2.The value of X can be obtained as 2,-1.
Statement alone is not sufficient

From 2) Similarly we get 2 equations x^2-x=2 and x^2+x=2 depeding upon whether X is positive or negative respectively which we dont know .
Statement 2 alone is not sufficient .
_________________

+1 if you like my explanation .Thanks :)

Kudos [?]: 376 [4], given: 51

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128527 [4], given: 12180

If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 02 Feb 2012, 05:44
4
This post received
KUDOS
Expert's post
10
This post was
BOOKMARKED
rohitgoel15 wrote:
If x is an integer, what is the value of x?
1) |x - |x2|| = 2
2) |x2 - |x|| = 2

I saw the solution and I think i cant even get close. On the test, I would prefer not to solve this question. But is there a short way to make an educated guess. :shock:


Answer is not E as given in above posts, it's C. Also note that 1 and -1 do not satisfy statement (2).

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2. First of all: \(|x^2|=x^2\) (as \(x^2\) is a non-negative value). Square both sides: \((x-x^2)^2=4\) --> factor out \(x\): \(x^2*(1-x)^2=4\) --> as \(x\) is an integer then \(x=2\) or \(x=-1\) (by trial and error: the product of two perfect square is 4: 1*4=4 or 4*1=4). Not sufficient.

(2) |x^2 - |x|| = 2 --> square both sides: \((x^2-|x|)^2=4\) --> factor out \(|x|\): \(x^2*(|x|-1)^2=4\) --> as \(x\) is an integer then \(x=2\) or \(x=-2\). Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is \(x=2\). Sufficient.

Answer: C.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128527 [4], given: 12180

Senior Manager
Senior Manager
avatar
Joined: 07 Nov 2009
Posts: 305

Kudos [?]: 685 [0], given: 20

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 03 Feb 2012, 09:46
Bunuel wrote:
rohitgoel15 wrote:
If x is an integer, what is the value of x?
1) |x - |x2|| = 2
2) |x2 - |x|| = 2

I saw the solution and I think i cant even get close. On the test, I would prefer not to solve this question. But is there a short way to make an educated guess. :shock:


Answer is not E as given in above posts, it's C. Also note that 1 and -1 does not satisfy statement (2).

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2. First of all: \(|x^2|=x^2\) (as \(x^2\) is a non-negative value). Square both sides: \((x-x^2)^2=4\) --> factor out \(x\): \(x^2*(1-x)^2=4\) --> as \(x\) is an integer then \(x=2\) or \(x=-1\) (by trial and error: the product of two perfect square is 4: 1*4=4 or 4*1=4). Not sufficient.

(2) |x2 - |x|| = 2 --> square both sides: \((x^2-|x|)^2=4\) --> factor out \(|x|\): \(x^2*(|x|-1)^2=4\) --> as \(x\) is an integer then \(x=2\) or \(x=-2\). Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is \(x=2\). Sufficient.

Answer: C.

Hope it's clear.


Thanks for the reply Bunuel. I didnt understand the factorization part in your post. It would be great if you can simplify the parts.
But is there a mistake in the below post?

amit2k9 wrote:
a.
squaring both sides we get
x^2 + x^4 - 2x* x^2 = 4
meaning, x^2 (x-1)^2 = 4
thus x = 2 | -1 not sufficient.

b same process and we get x = 2| -2
not sufficient.

a+b gives x = 2.

thus C it is.

Now take 1) |x - |x2|| = 2

|x2| is always positive. |x - |x2|| is negative since x^2>x

x^2-x=2.The value of X can be obtained as 2,-1.
Statement alone is not sufficient

From 2) Similarly we get 2 equations x^2-x=2 and x^2+x=2 depeding upon whether X is positive or negative respectively which we dont know .
Statement 2 alone is not sufficient .

Kudos [?]: 685 [0], given: 20

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128527 [0], given: 12180

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 03 Feb 2012, 10:16
Expert's post
1
This post was
BOOKMARKED
rohitgoel15 wrote:
Bunuel wrote:
rohitgoel15 wrote:
If x is an integer, what is the value of x?
1) |x - |x2|| = 2
2) |x2 - |x|| = 2

I saw the solution and I think i cant even get close. On the test, I would prefer not to solve this question. But is there a short way to make an educated guess. :shock:


Answer is not E as given in above posts, it's C. Also note that 1 and -1 does not satisfy statement (2).

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2. First of all: \(|x^2|=x^2\) (as \(x^2\) is a non-negative value). Square both sides: \((x-x^2)^2=4\) --> factor out \(x\): \(x^2*(1-x)^2=4\) --> as \(x\) is an integer then \(x=2\) or \(x=-1\) (by trial and error: the product of two perfect square is 4: 1*4=4 or 4*1=4). Not sufficient.

(2) |x2 - |x|| = 2 --> square both sides: \((x^2-|x|)^2=4\) --> factor out \(|x|\): \(x^2*(|x|-1)^2=4\) --> as \(x\) is an integer then \(x=2\) or \(x=-2\). Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is \(x=2\). Sufficient.

Answer: C.

Hope it's clear.


Thanks for the reply Bunuel. I didnt understand the factorization part in your post. It would be great if you can simplify the parts.
But is there a mistake in the below post?

amit2k9 wrote:
a.
squaring both sides we get
x^2 + x^4 - 2x* x^2 = 4
meaning, x^2 (x-1)^2 = 4
thus x = 2 | -1 not sufficient.

b same process and we get x = 2| -2
not sufficient.

a+b gives x = 2.

thus C it is.

Now take 1) |x - |x2|| = 2

|x2| is always positive. |x - |x2|| is negative since x^2>x

x^2-x=2.The value of X can be obtained as 2,-1.
Statement alone is not sufficient

From 2) Similarly we get 2 equations x^2-x=2 and x^2+x=2 depeding upon whether X is positive or negative respectively which we dont know .
Statement 2 alone is not sufficient .


First question: factoring out.
\((x-x^2)^2=4\) --> \((x*(1-x))^2=4\) --> \(x^2*(1-x)^2=4\);
\((x^2-|x|)^2=4\) --> now, we want to factor out \(|x|\) (notice x^2=|x|*|x| and we are factoring out one |x|) --> \((|x|*(|x|-1))^2=4\) --> \(x^2*(|x|-1)^2=4\).

Second question: other solutions.
amit2k9 corrected his solution after my post so the answer there is correct.
You also quote there saikarthikreddy's solution which I don't really understand as there are some parts in reasoning missing. Also it's not clear what is saikarthikreddy's answer. E? C?

Please ask if anything remains unclear in my post.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128527 [0], given: 12180

Manager
Manager
avatar
Joined: 02 Sep 2012
Posts: 245

Kudos [?]: 219 [0], given: 99

Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 18 Dec 2012, 21:04
Bunnel if you dont mind can you explain the factorizing part bit elaborately...Am totally not able to understand the second statement factorization
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Kudos [?]: 219 [0], given: 99

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128527 [1], given: 12180

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 19 Dec 2012, 03:13
1
This post received
KUDOS
Expert's post
skamal7 wrote:
Bunnel if you dont mind can you explain the factorizing part bit elaborately...Am totally not able to understand the second statement factorization


(2) |x^2 - |x|| = 2 --> square both sides: \((x^2-|x|)^2=4\). Since \(x^2=|x|^2\), then we have that \((|x|^2-|x|)^2=4\). Factor out \(|x|\): \(|x|^2*(|x|-1)^2=4\) --> \(x^2*(|x|-1)^2=4\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128527 [1], given: 12180

Intern
Intern
avatar
Joined: 05 Aug 2012
Posts: 17

Kudos [?]: 1 [0], given: 2

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 27 Dec 2012, 19:39
Bunuel wrote:
skamal7 wrote:
Bunnel if you dont mind can you explain the factorizing part bit elaborately...Am totally not able to understand the second statement factorization


(2) |x^2 - |x|| = 2 --> square both sides: \((x^2-|x|)^2=4\). Since \(x^2=|x|^2\), then we have that \((|x|^2-|x|)^2=4\). Factor out \(|x|\): \(|x|^2*(|x|-1)^2=4\) --> \(x^2*(|x|-1)^2=4\).



Hi Bunuel,

I understood what you did, what I didnt understand is why you squared the equation before simplifying it. What I knew about Mods, my line of reasoning is similar to what Apex231 did. I was just wondering about the approach that you took, squaring and then moving forward, clearly I am missing something here.. can you please explain.

Kudos [?]: 1 [0], given: 2

Current Student
User avatar
Joined: 27 Jun 2012
Posts: 405

Kudos [?]: 930 [0], given: 184

Concentration: Strategy, Finance
Re: If x is an integer... [#permalink]

Show Tags

New post 09 Jan 2013, 10:48
1) \(|x - |x^2|| = 2\)
Putting x as 2 -> \(|2 - 4| = 2\)
Putting x as -1 -> \(|-1 - 1| = 2\)
x has two values (2, -1)
Hence NOT SUFFICIENT.

2) \(|x^2 - |x|| = 2\)
Putting x as 2 -> \(|4 - 2| = 2\)
Putting x as -2 -> \(|4 - 3| = 2\)
x has two values (2, -2)
Hence NOT SUFFICIENT.

Combining 1 & 2 gives \(x =2\).
Hence (C) is the answer.

PS: how did we arrive into 2, -2, -1 roots?
Either pick numbers that are + or - integers or use algebraic approach below:

For choice 1 consider positive absolute value:
\(x - x^2 = 2\)
\(x^2 - x + 2 = 0\)
- no possible roots for this equation.

For choice 1 consider negative value:
\(-(x - x^2) = 2\)
\(x^2 - x -2 = 0\)
\(x = 2\) and \(x = -1\)
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
Reading Comprehension notes: Click here
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here
Looking to finance your tuition: Click here

Kudos [?]: 930 [0], given: 184

VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1377

Kudos [?]: 1674 [0], given: 62

Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: If x is an integer... [#permalink]

Show Tags

New post 09 Jan 2013, 10:59
sambam wrote:
If x is an integer, what is the value of x?

1) |x - |x^2|| = 2
2) |x^2 - |x|| = 2


A tough one indeed.
This question is not at all a sub-700 level question. IMO it is atleast 730 level question.

Statement 1 yields 2 cases, among which one provides non-real numbers. The two real number values of x are 2,-1.
Insufficient.

Statement 2 yields 4 cases as well, among which 2 provide non real numbers. The 2 real number solutions of x are (-2 and 1) and (2 and -1) respectively. One doesn't satisfies the statement 2 and thus is not considered.
3 values, hence insufficient.

The common value in statement 1 solution and statement 2 solution is -2.
Hence x=2 .
+1C
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Kudos [?]: 1674 [0], given: 62

VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1377

Kudos [?]: 1674 [0], given: 62

Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: If x is an integer... [#permalink]

Show Tags

New post 09 Jan 2013, 11:15
Please do proper search before posting.
This question has already been discussed at if-x-is-an-integer-what-is-the-value-of-x-126958.html.
Here are the rules for posting in the forum.
rules-for-posting-please-read-this-before-posting-133935.html.
Topic locked.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Kudos [?]: 1674 [0], given: 62

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 463

Kudos [?]: 197 [0], given: 134

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 07 Jul 2013, 17:08
If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2

|x - |x^2|| = 2
(x^2 is ALWAYS greater than or equal to zero so we can drop the absolute value sign)
|x-x^2| = 2
Two cases, positive and negative
Positive: x>1
x-x^2 = 2
-x^2 + x - 2 = 0
x^2 - x + 2 = 0
(can this be factored out?)

Negative: x<1
-x + x^2 = 2
x^2 - x -2 = 0
(x-2) * (x+1) = 0
x=2, x=-1

Here, we have two possible values for x.
INSUFFICIENT

(2) |x^2 - |x|| = 2

|x^2 - |x|| = 2
Two cases for x, positive and negative.
x>= 0
x^2 - x = 2
x^2 - x - 2 = 0
(x-2) * (x+1) = 0
x = 2, x = -1
two values, one less than zero one greater than zero.
INSUFFICIENT

x<0
x^2 - -x =2
x^2 + x - 2 = 0
(x+2) * (x-1) = 0
x=-2, x=1
two values for x but one is greater than zero and one is less than zero.
INSUFFICIENT

See, I would say E in this case. Where did I go wrong?

Solving it another way...

(1) |x - |x^2|| = 2
A stated above x^2 is greater than or equal to 0 so we can drop the absolute value signs.

(x-x^2)^2 = 4
x=2, x=-1

We get two values.
INSUFFICIENT

(2) |x^2 - |x|| = 2
As with #1 we can get rid of the outer absolute value signs by squaring.
|x^2 - |x|| = 2
(x^2 - |x|) = 2
(x^2 - |x|)^2 = 4
(remember, x^2 = |x|^2)
(|x|^2 - |x|)^2 = 4
|x|(|x| - 1)^2 = 4
x= 2, x=-2

we get two values
INSUFFICIENT

1+2 we get an intersection of x=-2
SUFFICIENT

Here is my question. There are many times where I have correctly used the first method (taking the positive and negative cases to solve) to solve problems and this seems like it could be one of those problems. Why is it that with this problem, that method appears to be incorrect?

Thanks!

Kudos [?]: 197 [0], given: 134

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128527 [0], given: 12180

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 07 Jul 2013, 23:26
WholeLottaLove wrote:
If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2

|x - |x^2|| = 2
(x^2 is ALWAYS greater than or equal to zero so we can drop the absolute value sign)
|x-x^2| = 2
Two cases, positive and negative
Positive: x>1
x-x^2 = 2
-x^2 + x - 2 = 0
x^2 - x + 2 = 0
(can this be factored out?)

Negative: x<1
-x + x^2 = 2
x^2 - x -2 = 0
(x-2) * (x+1) = 0
x=2, x=-1

Here, we have two possible values for x.
INSUFFICIENT

(2) |x^2 - |x|| = 2

|x^2 - |x|| = 2
Two cases for x, positive and negative.
x>= 0
x^2 - x = 2
x^2 - x - 2 = 0
(x-2) * (x+1) = 0
x = 2, x = -1
two values, one less than zero one greater than zero.
INSUFFICIENT

x<0
x^2 - -x =2
x^2 + x - 2 = 0
(x+2) * (x-1) = 0
x=-2, x=1
two values for x but one is greater than zero and one is less than zero.
INSUFFICIENT

See, I would say E in this case. Where did I go wrong?

Thanks!


This is not the best way to solve this question.

Also, notice that:
x-x^2<0 for x<0 and x>1 and
x-x^2>0 for 0<x<1.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128527 [0], given: 12180

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 463

Kudos [?]: 197 [0], given: 134

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 11 Jul 2013, 12:49
If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2

|x - |x^2|| = 2
(we can drop the inner absolute value signs because x^2 is always >= 0)
|x - x^2| = 2

Normally, there would be a positive and a negative case
Positive: 0<x<1
Negative: x>1, x<0

However, because x must be an integer, there is no positive case to test because only a fraction between 0 and 1 will provide a positive case.

Negative: x>1, x<0
|x - x^2| = 2
-(x-x^2) = 2
-x + x^2 = 2
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x=2, x=-1
Both values of x satisfy their given ranges (2>1 and -1<-0) So we are left with two possible correct answers
INSUFFICIENT

(2) |x^2 - |x|| = 2

|x^2 - |x|| = 2
Two cases:

X is an integer so it must be greater than or equal to 1 or less than or equal to -1. This means that |x^2 - |x|| = 2 will always be positive but |x| could be positive or negative.

|x^2 - |x|| = 2
x>0
(x^2 - x) = 2
x^2 - x - 2 = 0
(x - 2)(x + 1) = 0
x=2, x=-1
x=2 is Valid
OR
x<0
(x^2 - (-x)) = 2
x^2 + x - 2 = 0
(x + 2) (x - 1) = 0
x=-2, x=1
x=-2 is Valid

So, as with #1, we have two valid solutions for x, 2, -2

1+2) The valid solutions for #1 are 2 and -1, the valid solutions for #2 are 2 and -2. The only common number between them is 2.
SUFFICIENT


Could someone show me how to factor out both sides like Bunuel did in his explanation?

Thanks!

Kudos [?]: 197 [0], given: 134

Intern
Intern
avatar
Joined: 29 Oct 2013
Posts: 19

Kudos [?]: 14 [0], given: 8

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 25 Aug 2014, 06:23
Hey Bunuel,

I drew up the same solution but I chose E because after combining (1) and (2) I saw it as x=2 or x=-2 or x=1. Can you explain why this is wrong?

Kudos [?]: 14 [0], given: 8

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128527 [0], given: 12180

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 25 Aug 2014, 06:56
fra wrote:
Hey Bunuel,

I drew up the same solution but I chose E because after combining (1) and (2) I saw it as x=2 or x=-2 or x=1. Can you explain why this is wrong?


x = -1 does not satisfy either of the statements.
x = -2 does not satisfy the first statement.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128527 [0], given: 12180

Intern
Intern
avatar
Joined: 10 Sep 2014
Posts: 8

Kudos [?]: 2 [0], given: 86

GMAT 1: 750 Q49 V44
If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 10 Sep 2014, 05:45
Hey bunuel,
I got x=-1,2 from the first statement.
But in the second statement, i took positive and negative possibilities and came up with 4 equations.
the 4 equations are
1.(x^2)-x=2
2.(x^2)+x=2
3. -(x^2)+x=2
4. -(x^2)-x=2
Out of these four equations, according to me, only the 1st and the second have real solutions.
So from the 1st equation above i got x=-1,2(Same as the result from our First Statement )
and from the second equation i got x=1,-2.
But everywhere people have written that they got x=-2,2 from the second statement. Can you please explain it to me as to what the issue is.

Kudos [?]: 2 [0], given: 86

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128527 [1], given: 12180

Re: If x is an integer, what is the value of x? [#permalink]

Show Tags

New post 10 Sep 2014, 07:49
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
NikhilDev wrote:
Hey bunuel,
I got x=-1,2 from the first statement.
But in the second statement, i took positive and negative possibilities and came up with 4 equations.
the 4 equations are
1.(x^2)-x=2
2.(x^2)+x=2
3. -(x^2)+x=2
4. -(x^2)-x=2
Out of these four equations, according to me, only the 1st and the second have real solutions.
So from the 1st equation above i got x=-1,2(Same as the result from our First Statement )
and from the second equation i got x=1,-2.
But everywhere people have written that they got x=-2,2 from the second statement. Can you please explain it to me as to what the issue is.


Does -1, or 1 satisfy the equation? No. So, x cannot be -1 or 1.

Next, you get x^2 - x = 2 for positive x, so when solving you should discard negative solutions. Similarly, you get x^2 + x = 2 for negative x, so when solving you should discard positive solutions.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128527 [1], given: 12180

Re: If x is an integer, what is the value of x?   [#permalink] 10 Sep 2014, 07:49

Go to page    1   2    Next  [ 28 posts ] 

Display posts from previous: Sort by

If x is an integer, what is the value of x?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.