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

It is currently 30 Jul 2014, 21:45

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

Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1542
Followers: 5

Kudos [?]: 65 [1] , given: 39

Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1 [#permalink] New post 15 Aug 2009, 13:48
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

67% (01:49) correct 33% (01:15) wrong based on 52 sessions
Is x > 0?

(1) |x + 3| = 4x – 3

(2) |x + 1| = 2x – 1

guys.. try this one ...it's really good??!!
Intern
Intern
User avatar
Joined: 01 Aug 2009
Posts: 29
Location: Australia
Followers: 1

Kudos [?]: 13 [0], given: 3

Re: Good absolute value ds [#permalink] New post 16 Aug 2009, 08:08
IMO D.

Statement 1: x = 2
For (x+3) >= 0
x >= -3 [Not a solution as it doesn't satisfies the condition]
x+3=4x-3
x = 2

For (x+3) < 0
x < -3 [Not a solution as it doesn't satisfies the condition]
-(x+3) = 4x-3
x = 0 [Not a solution as it doesn't satisfies the condition]

Statement 2: x = 2
For (x+1) >= 0
x >= -1 [Not a solution as it doesn't satisfies the condition]
x+1 = 2x-1
x = 2

For (x+1) < 0
x < -1 [Not a solution as it doesn't satisfies the condition]
-(x+1) = 2x - 1
x = 0 [Not a solution as it doesn't satisfies the condition]

To save time, we should ignore all -ve cases of x as LHS is +ve and equal to RHS. So, for RHS to be positive x must be +ve.
_________________

The three most significant times in your life are:
1. When you fall in love
2. The birth of your first child
3. When you prepare for your GMAT

Senior Manager
Senior Manager
avatar
Joined: 17 Mar 2009
Posts: 310
Followers: 6

Kudos [?]: 232 [0], given: 22

GMAT Tests User
Re: Good absolute value ds [#permalink] New post 16 Aug 2009, 09:45
stmt1

|x+3| = 4x - 3
when |x+3|>0
x+3= 4x -3
3x-6=0
x=2

when |x+3|<0
-(x+3) = 4x-3
5x=0,x=0

not sufficient

stmt2
|x+1| = 2x - 1
when |x+1|>0
x+1=2x-1
x=2

when |x+1|<0
-(x+1)=2x-1
3x=0, x=0
not sufficient

is the answer E?
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3604
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 351

Kudos [?]: 1695 [0], given: 354

GMAT ToolKit User GMAT Tests User Premium Member
Re: Good absolute value ds [#permalink] New post 16 Aug 2009, 10:09
Expert's post
crejoc wrote:
stmt1
...
when |x+3|<0
-(x+3) = 4x-3
5x=0,x=0
....


Here is a typical mistake with moduli. You forgot to check your answer.
It is possible to use -(x+3) only if |x+3|<0 ! But at x=0, |0+3| > 0.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Senior Manager
Senior Manager
avatar
Joined: 17 Mar 2009
Posts: 310
Followers: 6

Kudos [?]: 232 [0], given: 22

GMAT Tests User
Re: Good absolute value ds [#permalink] New post 16 Aug 2009, 10:46
walker wrote:
crejoc wrote:
stmt1
...
when |x+3|<0
-(x+3) = 4x-3
5x=0,x=0
....


Here is a typical mistake with moduli. You forgot to check your answer.
It is possible to use -(x+3) only if |x+3|<0 ! But at x=0, |0+3| > 0.


thanks walker for pointing out the error,.. it was a stupid mistake..
Director
Director
User avatar
Joined: 25 Oct 2008
Posts: 611
Location: Kolkata,India
Followers: 8

Kudos [?]: 150 [0], given: 100

GMAT Tests User
Re: Good absolute value ds [#permalink] New post 23 Oct 2009, 17:28
The question stem asks is x>0??

Stmt 1:|x + 3| = 4x – 3
Two cases:
a. x+3=4x-3 ,x=0
b. -(x+3)=4x-3 ,x=0.

Both cases gives us x=0 hence SUFF.

Stmt 2:|x + 1| = 2x – 1
Again two cases:
a.x+1=2x-1
x-2x=-1-1
x=2

b. -(x+1)=2x-1
x=0
Both case gives us diff. values hence insuff. :(
IMO: A

Please point out my flaw.
_________________

countdown-beginshas-ended-85483-40.html#p649902

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18832
Followers: 3268

Kudos [?]: 22828 [3] , given: 2651

Re: Good absolute value ds [#permalink] New post 23 Oct 2009, 18:38
3
This post received
KUDOS
Expert's post
tejal777 wrote:
The question stem asks is x>0??

Stmt 1:|x + 3| = 4x – 3
Two cases:
a. x+3=4x-3 ,x=0
b. -(x+3)=4x-3 ,x=0.

Both cases gives us x=0 hence SUFF.

Stmt 2:|x + 1| = 2x – 1
Again two cases:
a.x+1=2x-1
x-2x=-1-1
x=2

b. -(x+1)=2x-1
x=0
Both case gives us diff. values hence insuff. :(
IMO: A

Please point out my flaw.



First you made a mistake in calculation: see the red part, solution there is x=2.
Second, which is more important the way of solving, from my point of view, is incorrect.

Let me share my way of thinking, step by step:

Is x > 0?
(1) |x + 3| = 4x – 3
As absolute value NEVER NEGATIVE (in our case |x + 3|), thus RHS in our case 4x-3 must be >=0.
4x-3>=0 --> x>=3/4 (you may think at this point that if the stem asks is x>0) that it's already sufficient, but it's not.

We should check if the equation |x + 3| = 4x – 3, with the condition that x>=3/4 has real roots.

x>=3/4 means that |x + 3|>0 so we'll have x+3=4x-3 --> x=2. Only ONE solution: x=2>0.
SUFFICIENT.

(2) |x + 1| = 2x – 1
The same here: 2x-1>=0 --> x>=1/2 --> only one possibility x+1=2x-1, x=2>0.
SUFFICIENT.

Answer: D.
_________________

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

Director
Director
User avatar
Joined: 25 Oct 2008
Posts: 611
Location: Kolkata,India
Followers: 8

Kudos [?]: 150 [0], given: 100

GMAT Tests User
Re: Good absolute value ds [#permalink] New post 23 Oct 2009, 18:42
Nice!Thank you so much!Kudos!:)
_________________

countdown-beginshas-ended-85483-40.html#p649902

Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 313
Followers: 2

Kudos [?]: 93 [0], given: 37

GMAT Tests User
Re: Good absolute value ds [#permalink] New post 23 Oct 2009, 19:03
I used substituting values as below and got D as answer:

S1)

|x+3| = 4x-3
when x=
-2 eq becomes 1 = -7 -->absurd
-1 eq becomes 2 = -7 -->absurd
0 eq becomes 3 = -3 -->absurd
1 eq becomes 5 = 5
2 eq becomes 6 = 9 -->absurd

so we can tell only x=2 satisifies the eq and hence S1 is sufficient.

similarly for S2)

|x+1| = 2x -1

when x =
-2 eq becomes 1 = -5 -->absurd
-1 eq becomes 0 = -3 -->absurd
0 eq becomes 1 = -1 -->absurd
1 eq becomes 2= 0 -->absurd
2 eq becomes 3 = 3
3 eq becomes 4 = 5 -->absurd

again we can tell x = 2 alone satisifes eq, hence S2 is sufficient.
Answer D.
_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Intern
Intern
avatar
Joined: 11 Dec 2012
Posts: 14
Followers: 0

Kudos [?]: 0 [0], given: 21

GMAT ToolKit User
Re: Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1 [#permalink] New post 09 Jan 2013, 10:03
One more easier exp.

Stmt (1)
First we squire both sides of the equality:
|x + 3| = 4x – 3
x^2+6x+9=16x^2-24x+9
15x^2-30x=0 divide both sides to 15
and we have:
x^2-2x=0
x(x-2)=0
x=0
but x=0 is not a root of the equation since |0 + 3| is not equal to 4*0 – 3= -3 because absolute value cannot equal to digit below zero
x-2=0
x=2 is a root of the equality, since |2 + 3| = 4*2 – 3=> 5 both sides
hence (1) is sufficient

stmt (2)
|x + 1| = 2x – 1
squire both sides again and we have:
x^2+2x+1=4x^2-4x+1
3x^2-6x=0, divide both sides to 3 and have:
X^2-2x=0
x(x-2)=0
x=0
but x=0 is not a root of the equation since |0 + 1| is not equal to 2*0 – 1= -1 because absolute value cannot equal to digit below zero
x-2=0
x=2 is a root of the equality, since |2 + 1| = 2*2 – 1=> 3 both sides

hence stmt (2) is sufficient

D
Re: Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1   [#permalink] 09 Jan 2013, 10:03
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Is (x - 4)(x - 3)(x + 2)(x + 1) > 0 HKHR 3 27 Sep 2013, 07:01
3 Experts publish their posts in the topic Is x > 0? (1) |x + 3| = 4x 3 (2) |x + 1| = 2x 1 Can rxs0005 11 03 Sep 2010, 13:20
Is x > 0? (1) |x + 3| = 4x 3 (2) |x 3| = |2x 3 alimad 11 24 Nov 2007, 05:37
Is x > 0? (1) |x + 3| = 4x 3 (2) |x 3| = |2x 3 jimjohn 8 31 Oct 2007, 06:49
Is x > 0? (1) |x + 3| = 4x 3 (2) |x 3| = |2x 3 iamba 8 01 Jul 2007, 08:52
Display posts from previous: Sort by

Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.