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

It is currently 22 Sep 2018, 18:25

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

M11-24

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
M11-24  [#permalink]

Show Tags

New post 16 Sep 2014, 00:45
3
12
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

54% (01:18) correct 46% (01:32) wrong based on 137 sessions

HideShow timer Statistics

Function \(F(x)\) is defined as follows:

if \(x\) is positive or 0 then \(F(x) = 1 - x\);

if \(x\) is negative then \(F(x) = x - 1\).

Which of the following is true about \(F(x)\)?

I. \(F(|x|) = |F(x)|\)

II. \(F(x) = F(-x)\)

III. \(|F(x + 1)| = |x|\)


A. I only
B. II only
C. III only
D. I and III only
E. not I, II, or III

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re M11-24  [#permalink]

Show Tags

New post 16 Sep 2014, 00:45
1
3
Official Solution:


Function \(F(x)\) is defined as follows:

if \(x\) is positive or 0 then \(F(x) = 1 - x\);

if \(x\) is negative then \(F(x) = x - 1\).

Which of the following is true about \(F(x)\)?

I. \(F(|x|) = |F(x)|\)

II. \(F(x) = F(-x)\)

III. \(|F(x + 1)| = |x|\)


A. I only
B. II only
C. III only
D. I and III only
E. not I, II, or III


I is not necessarily true. Consider \(x = -1\). \(F(|x|) = 0\) does not equal \(|F(x)| = 2\).

II is not necessarily true. Consider \(x = 1\). \(F(x) = 0\) does not equal \(F(-x) = -2\).

III is always true:

if \(x + 1\) is non-negative then \(|F(x + 1)| = |1 - (x + 1)| = |-x| = |x|\);

if \(x + 1\) is negative then \(|F(x + 1)| = |(x + 1) - 1| = |x|\)


Answer: C
_________________

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

Manager
Manager
User avatar
B
Joined: 12 Sep 2010
Posts: 234
Concentration: Healthcare, General Management
GMAT ToolKit User Reviews Badge
Re: M11-24  [#permalink]

Show Tags

New post 23 Oct 2014, 13:27
1
I think the question should be change to "Which of the following MUST be True about f(x)?" to make it more clear.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: M11-24  [#permalink]

Show Tags

New post 24 Oct 2014, 03:18
Samwong wrote:
I think the question should be change to "Which of the following MUST be True about f(x)?" to make it more clear.


Is true and must be true are the same and used interchangeably. Check the following problems from Official Guides:
in-the-figure-above-if-f-is-a-point-on-the-line-that-bisect-165054.html
m-is-the-sum-of-the-reciprocals-of-the-consecutive-integers-143703.html
if-a-0-3-which-of-the-following-is-true-143992.html
_________________

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

Manager
Manager
User avatar
B
Joined: 12 Sep 2010
Posts: 234
Concentration: Healthcare, General Management
GMAT ToolKit User Reviews Badge
Re: M11-24  [#permalink]

Show Tags

New post 24 Oct 2014, 12:41
Cool, I did not know that. Thank Bunuel for the reply.
Manager
Manager
avatar
Joined: 08 Feb 2014
Posts: 205
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)
Premium Member
Re: M11-24  [#permalink]

Show Tags

New post 12 Nov 2014, 21:39
Any quick approaches here? Plug and chug is taking me a bit too long...

Thanks
Retired Moderator
User avatar
P
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 527
GMAT ToolKit User
Re: M11-24  [#permalink]

Show Tags

New post 17 Jan 2015, 02:17
Bunuel wrote:
Official Solution:


Function \(F(x)\) is defined as follows:

if \(x\) is positive or 0 then \(F(x) = 1 - x\);

if \(x\) is negative then \(F(x) = x - 1\).

Which of the following is true about \(F(x)\)?

I. \(F(|x|) = |F(x)|\)

II. \(F(x) = F(-x)\)

III. \(|F(x + 1)| = |x|\)


A. I only
B. II only
C. III only
D. I and III only
E. not I, II, or III


I is not necessarily true. Consider \(x = -1\). \(F(|x|) = 0\) does not equal \(|F(x)| = 2\).

II is not necessarily true. Consider \(x = 1\). \(F(x) = 0\) does not equal \(F(-x) = -2\).

III is always true:

if \(x + 1\) is non-negative then \(|F(x + 1)| = |1 - (x + 1)| = |-x| = |x|\);

if \(x + 1\) is negative then \(|F(x + 1)| = |(x + 1) - 1| = |x|\)


Answer: C


Anyone to clarify the following? I don't understand this.

if x + 1 is non-negative then |F(x + 1)| = |1 - (x + 1)| = |-x| = |x|;

if x + 1 is negative then |F(x + 1)| = |(x + 1) - 1| = |x|

_________________

Hasan Mahmud

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: M11-24  [#permalink]

Show Tags

New post 17 Jan 2015, 17:00
Mahmud6 wrote:
Bunuel wrote:
Official Solution:


Function \(F(x)\) is defined as follows:

if \(x\) is positive or 0 then \(F(x) = 1 - x\);

if \(x\) is negative then \(F(x) = x - 1\).

Which of the following is true about \(F(x)\)?

I. \(F(|x|) = |F(x)|\)

II. \(F(x) = F(-x)\)

III. \(|F(x + 1)| = |x|\)


A. I only
B. II only
C. III only
D. I and III only
E. not I, II, or III


I is not necessarily true. Consider \(x = -1\). \(F(|x|) = 0\) does not equal \(|F(x)| = 2\).

II is not necessarily true. Consider \(x = 1\). \(F(x) = 0\) does not equal \(F(-x) = -2\).

III is always true:

if \(x + 1\) is non-negative then \(|F(x + 1)| = |1 - (x + 1)| = |-x| = |x|\);

if \(x + 1\) is negative then \(|F(x + 1)| = |(x + 1) - 1| = |x|\)


Answer: C


Anyone to clarify the following? I don't understand this.

if x + 1 is non-negative then |F(x + 1)| = |1 - (x + 1)| = |-x| = |x|;

if x + 1 is negative then |F(x + 1)| = |(x + 1) - 1| = |x|


We are told that:
if \(x\) is positive or 0 then \(F(x) = 1 - x\);
if \(x\) is negative then \(F(x) = x - 1\).

So,
if x + 1 is non-negative then |F(x + 1)| = |1 - (x + 1)| = |-x| = |x|;
if x + 1 is negative then |F(x + 1)| = |(x + 1) - 1| = |x|.
_________________

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: 16 May 2016
Posts: 3
Re: M11-24  [#permalink]

Show Tags

New post 11 Jul 2016, 07:16
Bunuel wrote:
Official Solution:


Function \(F(x)\) is defined as follows:

if \(x\) is positive or 0 then \(F(x) = 1 - x\);

if \(x\) is negative then \(F(x) = x - 1\).

Which of the following is true about \(F(x)\)?

I. \(F(|x|) = |F(x)|\)

II. \(F(x) = F(-x)\)

III. \(|F(x + 1)| = |x|\)


A. I only
B. II only
C. III only
D. I and III only
E. not I, II, or III


I is not necessarily true. Consider \(x = -1\). \(F(|x|) = 0\) does not equal \(|F(x)| = 2\).

II is not necessarily true. Consider \(x = 1\). \(F(x) = 0\) does not equal \(F(-x) = -2\).

III is always true:

if \(x + 1\) is non-negative then \(|F(x + 1)| = |1 - (x + 1)| = |-x| = |x|\);

if \(x + 1\) is negative then \(|F(x + 1)| = |(x + 1) - 1| = |x|\)


Answer: C



Hi Bunuel, the highlighted answer in red shouldn't be "2"?
As X=1, we should consider the positive branch of the function, so f(-x)=1-(-x) would result in f(-1)=1-(-1)=2.
Am I wrong?

Thanks!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: M11-24  [#permalink]

Show Tags

New post 11 Jul 2016, 07:21
RodrigoMi wrote:
Bunuel wrote:
Official Solution:


Function \(F(x)\) is defined as follows:

if \(x\) is positive or 0 then \(F(x) = 1 - x\);

if \(x\) is negative then \(F(x) = x - 1\).

Which of the following is true about \(F(x)\)?

I. \(F(|x|) = |F(x)|\)

II. \(F(x) = F(-x)\)

III. \(|F(x + 1)| = |x|\)


A. I only
B. II only
C. III only
D. I and III only
E. not I, II, or III


I is not necessarily true. Consider \(x = -1\). \(F(|x|) = 0\) does not equal \(|F(x)| = 2\).

II is not necessarily true. Consider \(x = 1\). \(F(x) = 0\) does not equal \(F(-x) = -2\).

III is always true:

if \(x + 1\) is non-negative then \(|F(x + 1)| = |1 - (x + 1)| = |-x| = |x|\);

if \(x + 1\) is negative then \(|F(x + 1)| = |(x + 1) - 1| = |x|\)


Answer: C



Hi Bunuel, the highlighted answer in red shouldn't be "2"?
As X=1, we should consider the positive branch of the function, so f(-x)=1-(-x) would result in f(-1)=1-(-1)=2.
Am I wrong?

Thanks!





If \(x = 1\). \(F(-x) =F(-1)\). We know that if \(x\) is negative then \(F(x) = x - 1\), thus \(F(-x) =F(-1)=-1-1=-2\).
_________________

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

Manager
Manager
User avatar
B
Joined: 23 Jun 2009
Posts: 196
Location: Brazil
GMAT 1: 470 Q30 V20
GMAT 2: 620 Q42 V33
GMAT ToolKit User Premium Member
Re: M11-24  [#permalink]

Show Tags

New post 03 Aug 2016, 16:18
birsencal wrote:
Please explain this in more detail



Hope it helps :)
>> !!!

You do not have the required permissions to view the files attached to this post.

Intern
Intern
avatar
B
Joined: 01 Nov 2017
Posts: 29
CAT Tests
Re: M11-24  [#permalink]

Show Tags

New post 02 Jul 2018, 21:41
Bunuel wrote:
Official Solution:

III is always true:

if \(x + 1\) is non-negative then \(|F(x + 1)| = |1 - (x + 1)| = |-x| = |x|\);

if \(x + 1\) is negative then \(|F(x + 1)| = |(x + 1) - 1| = |x|\)

Answer: C


I'm not following this at all. Can someone explain further? How do you get the 1 in 1-(x+1) for instance?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: M11-24  [#permalink]

Show Tags

New post 02 Jul 2018, 21:54
surfingpirate wrote:
Bunuel wrote:
Official Solution:

III is always true:

if \(x + 1\) is non-negative then \(|F(x + 1)| = |1 - (x + 1)| = |-x| = |x|\);

if \(x + 1\) is negative then \(|F(x + 1)| = |(x + 1) - 1| = |x|\)

Answer: C


I'm not following this at all. Can someone explain further? How do you get the 1 in 1-(x+1) for instance?


We are told that:
if \(x\) is positive or 0 then \(F(x) = 1 - x\);
if \(x\) is negative then \(F(x) = x - 1\).

So,
if x + 1 is non-negative then \(|F(x + 1)| = |1 - (x + 1)| = |-x| = |x|\);
if x + 1 is negative then \(|F(x + 1)| = |(x + 1) - 1| = |x|\).
_________________

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: 11 Feb 2017
Posts: 3
CAT Tests
Re: M11-24  [#permalink]

Show Tags

New post 07 Jul 2018, 04:56
Hi Brunnel,

Plz guide me where am I going wrong

for Option I : F (|x|) will always be equal to 1-x as |x| will always be greater than or equal to 0.

For x<0 : |F(x)| = |x-1|= |-(1-x)|= 1-x
For x>=0 : |F(x)| = |1-x| = 1-x

Therefore F (|x|) = |F(x)|

I understand you want me to try and negate the given must be condition. Can it be done algebraically without substitution ?
GMAT Club Bot
Re: M11-24 &nbs [#permalink] 07 Jul 2018, 04:56
Display posts from previous: Sort by

M11-24

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

Moderators: chetan2u, Bunuel

Events & Promotions

PREV
NEXT


Copyright

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®.