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

It is currently 14 Dec 2018, 11:28

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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

     December 14, 2018

     December 14, 2018

     10:00 PM PST

     11:00 PM PST

    Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
  • Free GMAT Strategy Webinar

     December 15, 2018

     December 15, 2018

     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.

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

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

Hide Tags

Manager
Manager
User avatar
P
Joined: 24 Oct 2016
Posts: 241
GMAT 1: 670 Q46 V36
Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1  [#permalink]

Show Tags

New post 02 Aug 2018, 09:47
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:32) correct 48% (01:43) wrong based on 50 sessions

HideShow timer Statistics

Is x > 0?


(1) |x + 3| = 4x – 3

(2) |x + 1| = 2x – 1

_________________

Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW)
Verb Tenses Simplified

If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.

Manager
Manager
User avatar
P
Joined: 24 Oct 2016
Posts: 241
GMAT 1: 670 Q46 V36
Re: Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1  [#permalink]

Show Tags

New post 02 Aug 2018, 09:50
1
dabaobao wrote:
Is x > 0?

(1) |x + 3| = 4x – 3

(2) |x + 1| = 2x – 1



(1) SUFFICIENT: Here, we are told that |x + 3| = 4x – 3. When dealing with equations containing variables and absolute values, we generally need to consider the possibility that there may be two values for the unknown that could make the equation work. 
We can find the two possible solutions by setting the expression inside the absolute value equal to ± the expression on the right side of the equation. In this case, our two solutions are: 

x + 3 = +(4x – 3)       and      x + 3 = –(4x – 3) 
x + 3 = 4x – 3                       x + 3 = –4x + 3 
6 = 3x                                  5x = 0 
2 = x                                    x = 0 

However, you need to be careful. When there is a variable outside the absolute value, both solutions are not always valid. We need to plug both x = 2 and x = 0 back into the original equation and test them. 

|(2) + 3| = 4(2) – 3    and      |(0) + 3| = 4(0) – 3 
|5| = 8 – 3                            |3| = –3 
5 = 5                                    3 = –3 

Therefore, x = 0 is not a valid solution and we know that 2 is the only possible solution. x is definitely positive. 

(2) SUFFICIENT: Here, again, we must consider the two possible solutions for the absolute value expression. They are: 

x + 1 = +(2x – 1)       and      x + 1 = –(2x – 1) 
x + 1 = 2x – 1                       x + 1 = –2x + 1 
2 = x                                    3x = 0 
                                            x = 0 

Once again, we need to verify that both solutions are valid. We need to plug x = 2 and x = 0 into the original equation: 

|(2) + 1| = 2(2) – 1    and      |(0) + 1| = 2(0) – 1 
|3| = 4 – 1                            |1| = –1 
3 = 3                                    1 = –1 

One again, 2 is the only valid solution and we can determine that x is positive. 

The correct answer is D. (OE: Manhattan Prep)
_________________

Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW)
Verb Tenses Simplified

If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51215
Re: Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1  [#permalink]

Show Tags

New post 02 Aug 2018, 23:05
2
dabaobao wrote:
dabaobao wrote:
Is x > 0?

(1) |x + 3| = 4x – 3

(2) |x + 1| = 2x – 1



(1) SUFFICIENT: Here, we are told that |x + 3| = 4x – 3. When dealing with equations containing variables and absolute values, we generally need to consider the possibility that there may be two values for the unknown that could make the equation work. 
We can find the two possible solutions by setting the expression inside the absolute value equal to ± the expression on the right side of the equation. In this case, our two solutions are: 

x + 3 = +(4x – 3)       and      x + 3 = –(4x – 3) 
x + 3 = 4x – 3                       x + 3 = –4x + 3 
6 = 3x                                  5x = 0 
2 = x                                    x = 0 

However, you need to be careful. When there is a variable outside the absolute value, both solutions are not always valid. We need to plug both x = 2 and x = 0 back into the original equation and test them. 

|(2) + 3| = 4(2) – 3    and      |(0) + 3| = 4(0) – 3 
|5| = 8 – 3                            |3| = –3 
5 = 5                                    3 = –3 

Therefore, x = 0 is not a valid solution and we know that 2 is the only possible solution. x is definitely positive. 

(2) SUFFICIENT: Here, again, we must consider the two possible solutions for the absolute value expression. They are: 

x + 1 = +(2x – 1)       and      x + 1 = –(2x – 1) 
x + 1 = 2x – 1                       x + 1 = –2x + 1 
2 = x                                    3x = 0 
                                            x = 0 

Once again, we need to verify that both solutions are valid. We need to plug x = 2 and x = 0 into the original equation: 

|(2) + 1| = 2(2) – 1    and      |(0) + 1| = 2(0) – 1 
|3| = 4 – 1                            |1| = –1 
3 = 3                                    1 = –1 

One again, 2 is the only valid solution and we can determine that x is positive. 

The correct answer is D. (OE: Manhattan Prep)


This question has MUCH easier solution.

Is x > 0?

(1) \(|x+3|=4x-3\) --> LHS is an absolute value, which is always non-negative (\(|some \ expression|\geq{0}\)), so RHS must also be non-negative --> \(4x-3\geq{0}\) --> \(x\geq{\frac{3}{4}}\), hence \(x>0\). Sufficient. You can see here that you don't even need to find exact value(s) of x to answer the question.

(2) \(|x + 1| = 2x – 1\). The same here. LHS is an absolute value, which is always non-negative (\(|some \ expression|\geq{0}\)), so RHS must also be non-negative --> \(2x-1\geq{0}\) --> \(x\geq{\frac{1}{2}}\), hence \(x>0\). Sufficient.

Answer: D.
_________________

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

GMAT Club Bot
Re: Is x > 0? (1) |x + 3| = 4x – 3 (2) |x + 1| = 2x – 1 &nbs [#permalink] 02 Aug 2018, 23:05
Display posts from previous: Sort by

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

  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®.