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

It is currently 17 Jan 2019, 12:21

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 in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winning strategy for a high GRE score

     January 17, 2019

     January 17, 2019

     08:00 AM PST

     09:00 AM PST

    Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

How many integers x are there so that |x-3.5 | < 2

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

Hide Tags

 
Manager
Manager
User avatar
S
Joined: 13 Oct 2013
Posts: 139
Concentration: Strategy, Entrepreneurship
GMAT ToolKit User Premium Member CAT Tests
How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 11 Nov 2014, 09:12
1
5
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

70% (00:46) correct 30% (00:53) wrong based on 616 sessions

HideShow timer Statistics

How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52231
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 11 Nov 2014, 09:21
2
1
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

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
S
Joined: 13 Oct 2013
Posts: 139
Concentration: Strategy, Entrepreneurship
GMAT ToolKit User Premium Member CAT Tests
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 11 Nov 2014, 09:28
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2




Bunuel wrote:
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52231
How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 11 Nov 2014, 09:35
sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2




Bunuel wrote:
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C


Let me ask you a question how does |x| < 1 translate?
_________________

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
S
Joined: 13 Oct 2013
Posts: 139
Concentration: Strategy, Entrepreneurship
GMAT ToolKit User Premium Member CAT Tests
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 11 Nov 2014, 10:11
-1<x<1

ok now i got it:).thank you



sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2




Bunuel wrote:
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 416
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post Updated on: 14 Jan 2015, 02:40
I guess this is the same as doing this?

|x-3.5|<2
x-3.5<2
x<5.5 and,

-x+3.5<2
-x<2-3.5
-x<-1.5
x>1.5

Both together:
1.5<x<5.5

So, x can be 1.5, 2.5, 3.5 or 4.5 (0r in fact 2,3,4,5 since it is an integer). Is this the solution?

Originally posted by pacifist85 on 14 Jan 2015, 02:36.
Last edited by pacifist85 on 14 Jan 2015, 02:40, edited 2 times in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52231
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 14 Jan 2015, 02:40
pacifist85 wrote:
I guess this is the same as doing this?

|x-3.5|<2
x-3.5<2
x<5.5 and,

-x+3.5<2
-x<2-3.5
-x<-0.5
x>0.5


Both together:
0.5<x<5.5

So, x can be: 1.5, 2.5, 3.5 or 4.5 (0r 1,2,3,4 since it is an integer). Is this the solution?


-x < 2 - 3.5
x > 1.5.

For complete solution please read how-many-integers-x-are-there-so-that-x-188429.html#p1441230
_________________

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
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 416
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 14 Jan 2015, 02:42
Yes thank you Bunuel,

I copied it wrong from my notebook..
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13331
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 14 Jan 2015, 22:39
Hi All,

Sometimes the easiest/fastest way to get to the correct answer is to use "brute force" - you can literally just jam numbers into this question until you physically find all of the answers. Children can do it, so you can do it.

The prompt asks for all of the INTEGER values of X that fit |X - 3.5| < 2. From the answer choices, we know that there are at least 2, but no more than 6, possibilities.

The first answer you will find is probably the easiest: X = 4

|4 - 3.5| = .5 which IS < 2

Now, let's go "bigger"
X = 5
|5 - 3.5| = 1.5 which IS < 2

X = 6 gives us...
|6 - 3.5| = 2.5 which is TOO BIG. So X CANNOT be 6 and it CANNOT be > 6

Let's go "smaller" (from X = 4)

X = 3
|3 - 3.5| = |-.5| = .5 which IS < 2

X = 2
|2 - 3.5| = |-1.5| = 1.5 which IS < 2

X = 1
|1 - 3.5| = |-2.5| = 2.5 which is TOO BIG. So X CANNOT be 1 and it CANNOT be < 1.

The values of X that "fit" are 2, 3, 4, and 5 --> 4 integers.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Director
Director
User avatar
B
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 517
CAT Tests
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 14 Apr 2015, 21:23
sunita123 wrote:
Thanks Bunuel,
But I did not understand this part

|x-3.5| < 2 means that -2 <| x-3.5 |< 2




Bunuel wrote:
sunita123 wrote:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?

A. 2
B. 3
C. 4
D. 5
E. 6

M10-01


\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\). Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\). Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.

Answer: C


The rule is : lxl<a
=>, -a<x<a

Here, x=x - 3.5 and a=2
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 937
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 22 Jun 2017, 21:25
|x-3.5 | < 2

-2 < x - 3.5 < 2

1.5 < x < 5.5

As per above statement, and as x is an integer.

x can take values of 2,3,4 & 5

Hence, Answer is C
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9418
Premium Member
Re: How many integers x are there so that |x-3.5 | < 2  [#permalink]

Show Tags

New post 01 Nov 2018, 10:38
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: How many integers x are there so that |x-3.5 | < 2 &nbs [#permalink] 01 Nov 2018, 10:38
Display posts from previous: Sort by

How many integers x are there so that |x-3.5 | < 2

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


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®.