Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Sep 2014, 10:08

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many possible integer values are there for x if |4x - 3|

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 19 Nov 2004
Posts: 45
Followers: 0

Kudos [?]: 4 [1] , given: 0

How many possible integer values are there for x if |4x - 3| [#permalink] New post 19 Dec 2004, 17:33
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

58% (01:58) correct 42% (00:54) wrong based on 421 sessions
How many possible integer values are there for x if |4x - 3| < 6 ?

A. One
B. Two
C. Three
D. Four
E. Five

[Reveal] Spoiler:
What I did here was to separate two scenarios:
a. 4x – 3 < 6 and
b. 4x – 3 > - 6

I simplified x in both scenarios that I ended up in a range of -2.25 < x < .75
Therefore, my answer is 3 integers (-2, -1, 0)

I would like to know if this method is correct and if I should use such method for problems that involve absolute value and inequality.
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Oct 2013, 03:03, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Manager
User avatar
Joined: 26 Dec 2003
Posts: 227
Location: India
Followers: 1

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

 [#permalink] New post 19 Dec 2004, 21:34
u can do this way. Directly substitute the value of x by trial and error method . Start from 0 and move on. u will get 0,1 and 2 as it asked for positive integers
1 KUDOS received
Manager
Manager
avatar
Joined: 19 Nov 2004
Posts: 59
Followers: 1

Kudos [?]: 3 [1] , given: 0

 [#permalink] New post 21 Dec 2004, 03:21
1
This post received
KUDOS
Cpcalanoc you choose the right way BUT from 4x-3<6 => 4x<9 =>
x<2.25
the same mistake in the other

So -0.75 < x < 2.25
then the answer (0, 1, 2)

to Rakesh1239 your answer is right but where you see the word positive?
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2546
Followers: 200

Kudos [?]: 40 [0], given: 0

Premium Member
Re: How many possible integer values are there for x, if I 4x 3 [#permalink] New post 19 Oct 2013, 22:28
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

Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23063
Followers: 3537

Kudos [?]: 27224 [5] , given: 2725

Re: How many possible integer values are there for x if |4x - 3| [#permalink] New post 20 Oct 2013, 03:08
5
This post received
KUDOS
Expert's post
How many possible integer values are there for x if |4x - 3| < 6 ?

A. One
B. Two
C. Three
D. Four
E. Five

|4x - 3| < 6;

Get rid of the modulus: -6<4x-3< 6;

Add 3 to all three parts: -3<4x< 9;

Divide by 4: -\frac{3}{4}<x< \frac{9}{4} --> -0.75<x< 2.25.

x can take following integer values: 0, 1, and 2.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1667
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 13

Kudos [?]: 167 [0], given: 276

GMAT ToolKit User
Re: How many possible integer values are there for x if |4x - 3| [#permalink] New post 20 Nov 2013, 04:25
cpcalanoc wrote:
How many possible integer values are there for x if |4x - 3| < 6 ?

A. One
B. Two
C. Three
D. Four
E. Five

[Reveal] Spoiler:
What I did here was to separate two scenarios:
a. 4x – 3 < 6 and
b. 4x – 3 > - 6

I simplified x in both scenarios that I ended up in a range of -2.25 < x < .75
Therefore, my answer is 3 integers (-2, -1, 0)

I would like to know if this method is correct and if I should use such method for problems that involve absolute value and inequality.


You can try algebraically, If x>=0, then you will have the range 0<=x<9/4
If x<0, you get x>3/4 but this solution is not valid so x must vbe x>=0. Hence, you have 3 integer solutions from the above inequality: 0, 1 and 2.

Hope this helps
Cheers
J :)
Manager
Manager
User avatar
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 94
Location: India
Concentration: Finance, Strategy
GMAT Date: 10-31-2014
GPA: 3.5
WE: Consulting (Computer Hardware)
Followers: 0

Kudos [?]: 13 [0], given: 35

CAT Tests
Re: How many possible integer values are there for x if |4x - 3| [#permalink] New post 26 Mar 2014, 08:06
[quote="cpcalanoc"]How many possible integer values are there for x if |4x - 3| < 6 ?

A. One
B. Two
C. Three
D. Four
E. Five

Solution: |4x-3| < 6

let 4x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left

(the less than sign represents that the a must be within boundaries )

(3-6)----------3----------(3+6)

now, we have -3<a<9

but a =4x ==> -3<4x<9

dividing all values by +4 we have -0.75 <x < 2.24

Now question says Integer values (not rational ) therefore we have 0,1,2

Hence 3
Manager
Manager
avatar
Joined: 25 Mar 2013
Posts: 82
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Followers: 0

Kudos [?]: 9 [0], given: 45

Re: How many possible integer values are there for x if |4x - 3| [#permalink] New post 11 Apr 2014, 06:29
My Strategy , X is an integer ( + , - , 0 )
Principles : Integers ,Module and Inequality
Plug In Method Start with 0 , 1 , -1 , 2 as values
By Plugging in |4x - 3| < 6 Is Yes for 0 , 1, 2 But not with -1 So 3 Values :)

After seeing Bunnel solution we can use Module Basics with a Range in Number line
-6<4x - 3< 6 , -3<4x<9 , \frac {3}{4} <x< \frac{9}{4}, So - 0,75<x< 2.25
So Range from 0 , 1 , 2


If any wrong or any Suggestions in my Strategy pls Correct it
Intern
Intern
avatar
Joined: 10 Apr 2014
Posts: 33
Followers: 0

Kudos [?]: 17 [0], given: 3

Re: How many possible integer values are there for x if |4x - 3| [#permalink] New post 11 Apr 2014, 11:12
kanusha wrote:
My Strategy , X is an integer ( + , - , 0 )
Principles : Integers ,Module and Inequality
Plug In Method Start with 0 , 1 , -1 , 2 as values
By Plugging in |4x - 3| < 6 Is Yes for 0 , 1, 2 But not with -1 So 3 Values :)

After seeing Bunnel solution we can use Module Basics with a Range in Number line
-6<4x - 3< 6 , -3<4x<9 , \frac {3}{4} <x< \frac{9}{4}, So - 0,75<x< 2.25
So Range from 0 , 1 , 2


If any wrong or any Suggestions in my Strategy pls Correct it



your strategy is good but suppose if you have lot of integers, how many will you keep plugging?

The second method is better as you quickly know the range and based on conceptual understanding.

given 4x - 3 can take both positive and negative values. It can lie between -6 and 0 or 0 and +6.
Intern
Intern
avatar
Joined: 08 Sep 2010
Posts: 39
Followers: 1

Kudos [?]: 5 [0], given: 11

Re: How many possible integer values are there for x if |4x - 3| [#permalink] New post 27 Apr 2014, 08:58
Bunuel wrote:
How many possible integer values are there for x if |4x - 3| < 6 ?

A. One
B. Two
C. Three
D. Four
E. Five

|4x - 3| < 6;

Get rid of the modulus: -6<4x-3< 6;

Add 3 to all three parts: -3<4x< 9;

Divide by 4: -\frac{3}{4}<x< \frac{9}{4} --> -0.75<x< 2.25.

x can take following integer values: 0, 1, and 2.

Answer: C.



@Bunuel - The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0).
Am I missing anything here?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23063
Followers: 3537

Kudos [?]: 27224 [0], given: 2725

Re: How many possible integer values are there for x if |4x - 3| [#permalink] New post 28 Apr 2014, 00:34
Expert's post
chanakya84 wrote:
Bunuel wrote:
How many possible integer values are there for x if |4x - 3| < 6 ?

A. One
B. Two
C. Three
D. Four
E. Five

|4x - 3| < 6;

Get rid of the modulus: -6<4x-3< 6;

Add 3 to all three parts: -3<4x< 9;

Divide by 4: -\frac{3}{4}<x< \frac{9}{4} --> -0.75<x< 2.25.

x can take following integer values: 0, 1, and 2.

Answer: C.



@Bunuel - The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0).
Am I missing anything here?


The question does not specify that the integers must be positive: "how many possible integer values are there for x..."

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 08 Sep 2010
Posts: 39
Followers: 1

Kudos [?]: 5 [0], given: 11

Re: How many possible integer values are there for x if |4x - 3| [#permalink] New post 28 Apr 2014, 05:46
Bunuel wrote:
chanakya84 wrote:
Bunuel wrote:
How many possible integer values are there for x if |4x - 3| < 6 ?

A. One
B. Two
C. Three
D. Four
E. Five

|4x - 3| < 6;

Get rid of the modulus: -6<4x-3< 6;

Add 3 to all three parts: -3<4x< 9;

Divide by 4: -\frac{3}{4}<x< \frac{9}{4} --> -0.75<x< 2.25.

x can take following integer values: 0, 1, and 2.

Answer: C.



@Bunuel - The question stems talks about how many positive integer values of x. IF we are talking about positive integer then it should be only {1,2} and not {0).
Am I missing anything here?


The question does not specify that the integers must be positive: "how many possible integer values are there for x..."

Hope it's clear.


Ahh..my mistake....
Read the question wrong.
Re: How many possible integer values are there for x if |4x - 3|   [#permalink] 28 Apr 2014, 05:46
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic How many integral values of X will satisfy |x-3|+|2x+4|+|x|< email2vm 3 25 Mar 2014, 10:47
3 Experts publish their posts in the topic If 5 - 6/x = x, then x has how many possible values? Walkabout 5 29 Dec 2012, 06:07
4 Experts publish their posts in the topic If 4/x < 1/3 , what is the possible range of values of x? harshvinayak 12 25 Aug 2012, 00:47
If 4/x <1/3, what is the possible range of values for x? GMATD11 4 07 Apr 2011, 04:01
4 How many integral values of k are possible, if the lines 3x+ vjsharma25 7 09 Mar 2011, 22:43
Display posts from previous: Sort by

How many possible integer values are there for x if |4x - 3|

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.