GMAT Question of the Day - Daily to your Mailbox; hard ones only
close

It is currently 23 Jun 2018, 11:05
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

M08-11

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
First unread post
Author Message
TAGS:

Hide Tags
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Premium Member CAT Tests
Top Member of the Month
M08-11 [#permalink]

Show Tags

New post 16 Sep 2014, 00:37
5
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

47% (01:22) correct 53% (01:19) wrong based on 105 sessions

HideShow timer Statistics

Is \(|x - 1| \lt 1\) ?


(1) \((x - 1)^2 \le 1\)

(2) \(x^2 - 1 \gt 0\)
Spoiler: OA

_________________

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Premium Member CAT Tests
Top Member of the Month
Re M08-11 [#permalink]

Show Tags

New post 16 Sep 2014, 00:37
3
Official Solution:


(1) \((x - 1)^2 \le 1\). Since both sides of the inequality are non-negative then we can take square root from both parts: \(|x-1| \le 1\), so \(|x-1|\) can be less than 1 (answer YES), as well as equal to 1, for \(x=2\) or \(x=0\) (answer NO). Not sufficient. Notice that \(|x-1| \le 1\), means \(0 \le x \le 2\).

(2) \(x^2 - 1 \gt 0\). Rearrange: \(x^2 \gt 1\). Again, since both sides of the inequality are non-negative then we can take square root from both parts: \(|x| \gt 1\). If \(x=1.5\) then the answer is YES but if \(x=2\) then the answer is NO. Not sufficient.

(1)+(2) \(x=1.5\) and \(x=2\) satisfy both statements and give different answer to the question. Not sufficient.


Answer: E
_________________

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

Intern
Intern
User avatar
Joined: 22 Aug 2014
Posts: 45
GMAT ToolKit User
M08-11 [#permalink]

Show Tags

New post 20 Jan 2016, 06:54
Is |x−1|<1 ?
(1) (x−1)^2≤1
(2) x^2−1>0
First,though it sounds absurd, try to test the condition whether sufficient or not even without using (1) or (2),. Place 5, 4<1, answer is no. Again, place -2, 3<1..still no. Now, place 2,1<1..still no.Now place 1, now we get the answer yes for 0<1. again, place 0, we get 1<1, no. So, once yes, once no suggests we need more data!
Now take (1) whether we get constant yes or constant no. By rooting, we get |x−1|≤1, means 0≤x≤2. Now we have restricted freedom to choose value. We can't choose any value less than 0 or more than 2. Lets try within this boundary. Place 0 or 2, we get 1 but is 1 less than 1?,NO. Try 1, |x−1|=0 (<1), YES,now less than 1. So, insufficient because of both outcome. We need either yes or no, not both simultaneously.
Think solely on (2) now.x^2−1>0;|x|>1. so, we have to take such values either greater than 1 or less than -1. Any less than -1 value makes |x−1| more than 1, so NO. In addition, placing any value 2 or more than 2 gives us same NO. Whatif, we try placing values within 0 to 1;say,1.5. we get |x−1|=.5(<1),so YES. Once yes,once no suggests insufficient.[if x were integer, (2) would be sufficient alone]
Now combine (1) and (2). (1) restricts the freedom to choose within 0≤x≤2. (2) restricts it by |x|>1.Even after combining, nothing changes.Still we can put 1<x≤2. Try putting 2, answer NO. Try putting 1.5, YES. So, combining still fails to give a reliable or constant answer.
Intern
Intern
avatar
Joined: 29 Jan 2015
Posts: 9
Re M08-11 [#permalink]

Show Tags

New post 02 Feb 2016, 11:14
Hi - For this question, Stmt1 solutions assumed inequality is less than equal to. Hence solutions states 0<= x <= 2 but it should be 0 < x < 2 which will make stmt 1 Sufficient. Please confirm?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Premium Member CAT Tests
Top Member of the Month
Re: M08-11 [#permalink]

Show Tags

New post 02 Feb 2016, 11:18
fydpoctave wrote:
Hi - For this question, Stmt1 solutions assumed inequality is less than equal to. Hence solutions states 0<= x <= 2 but it should be 0 < x < 2 which will make stmt 1 Sufficient. Please confirm?


Why should it be 0 < x < 2 ? Both 0 and 2 satisfy \((x−1)^2≤1\).
_________________

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

Intern
Intern
avatar
Joined: 29 Jan 2015
Posts: 9
Re: M08-11 [#permalink]

Show Tags

New post 02 Feb 2016, 11:21
Bunuel wrote:
fydpoctave wrote:
Hi - For this question, Stmt1 solutions assumed inequality is less than equal to. Hence solutions states 0<= x <= 2 but it should be 0 < x < 2 which will make stmt 1 Sufficient. Please confirm?


Why should it be 0 < x < 2 ? Both 0 and 2 satisfy \((x−1)^2≤1\).


Sorry should have clarified. I was referring to question stem (following part from the solution)

Notice that |x−1|≤1, means 0≤x≤2.

But question has |x−1|<1 only
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Premium Member CAT Tests
Top Member of the Month
Re: M08-11 [#permalink]

Show Tags

New post 02 Feb 2016, 11:29
fydpoctave wrote:
Bunuel wrote:
fydpoctave wrote:
Hi - For this question, Stmt1 solutions assumed inequality is less than equal to. Hence solutions states 0<= x <= 2 but it should be 0 < x < 2 which will make stmt 1 Sufficient. Please confirm?


Why should it be 0 < x < 2 ? Both 0 and 2 satisfy \((x−1)^2≤1\).


Sorry should have clarified. I was referring to question stem (following part from the solution)

Notice that |x−1|≤1, means 0≤x≤2.

But question has |x−1|<1 only


Please read the solution carefully:

Statement 1 - \((x−1)^2≤1\) is equivalent to \(|x−1|≤1\), which translates to \(0≤x≤2\).
_________________

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

Senior Manager
Senior Manager
User avatar
Joined: 31 Mar 2016
Posts: 401
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)
GMAT ToolKit User Premium Member
Re M08-11 [#permalink]

Show Tags

New post 20 Aug 2016, 04:57
I think this is a high-quality question and I agree with explanation.
Intern
Intern
avatar
B
Joined: 07 Feb 2016
Posts: 21
GMAT 1: 650 Q47 V34
GMAT 2: 710 Q48 V39
Re: M08-11 [#permalink]

Show Tags

New post 07 May 2017, 02:06
Am I correct, that if statement 1) mentions \((x-1)^2<1\) instead of \((x-1)^2≤1\) that both statements together would be sufficient?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Premium Member CAT Tests
Top Member of the Month
Re: M08-11 [#permalink]

Show Tags

New post 07 May 2017, 02:19
ChrisL1988 wrote:
Am I correct, that if statement 1) mentions \((x-1)^2<1\) instead of \((x-1)^2≤1\) that both statements together would be sufficient?


In this case the first statement itself would be sufficient because \((x-1)^2<1\) is the same as \(|x-1|<1\) (by taking the square root).
_________________

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

Intern
Intern
avatar
B
Joined: 07 Feb 2016
Posts: 21
GMAT 1: 650 Q47 V34
GMAT 2: 710 Q48 V39
Re: M08-11 [#permalink]

Show Tags

New post 07 May 2017, 02:21
Bunuel wrote:
ChrisL1988 wrote:
Am I correct, that if statement 1) mentions \((x-1)^2<1\) instead of \((x-1)^2≤1\) that both statements together would be sufficient?


In this case the first statement itself would be sufficient because \((x-1)^2<1\) is the same as \(|x-1|<1\) (by taking the square root).


Of course, you are right, my fault. Thank you for the quick reply!
Intern
Intern
avatar
B
Joined: 02 Mar 2017
Posts: 1
Re: M08-11 [#permalink]

Show Tags

New post 30 Sep 2017, 07:15
why the negative value of x in case of 2nd statement i.e x < -1 not considered while solving?
for eg wen x > 1, it is not sufficient. but when x< -1, in every case the eq exceeds 1 and therefore it is sufficient to solve. By this logic optn 2 shud be sufficient right?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Premium Member CAT Tests
Top Member of the Month
Re: M08-11 [#permalink]

Show Tags

New post 30 Sep 2017, 07:19
Kunal14792 wrote:
why the negative value of x in case of 2nd statement i.e x < -1 not considered while solving?
for eg wen x > 1, it is not sufficient. but when x< -1, in every case the eq exceeds 1 and therefore it is sufficient to solve. By this logic optn 2 shud be sufficient right?


In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

We can get both an YES and a NO answers for the second statement (even not considering negative numbers) hence the statement is not sufficient.
_________________

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

Re: M08-11   [#permalink] 30 Sep 2017, 07:19
Print view
First unread post
Display posts from previous: Sort by

M08-11

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

Moderators: chetan2u, Bunuel

Search for:


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions