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

It is currently 18 Oct 2018, 15:38

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

What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1

  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: 50000
What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 24 Apr 2017, 04:21
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

43% (01:09) correct 57% (00:55) wrong based on 277 sessions

HideShow timer Statistics

Most Helpful Community Reply
SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1836
Reviews Badge CAT Tests
What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 24 Apr 2017, 14:04
5
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7


Hi Max,

When you deal with such statement, you need to add extra step. You need to check the solutions you get in the original equation.

x =-7, substitute in original equation: |2x − 1| = 3x + 6

|-14 − 1| = -21 + 6......15=-15.........so, x=-7 is not viable solution.

x=-1
|- 3| = 3........3=3..............so x=-1 is viable solution

So we have only one answer.
General Discussion
Intern
Intern
avatar
Joined: 20 Apr 2017
Posts: 4
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 24 Apr 2017, 04:33
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Statement 2:
x²=1

x could either be 1 or -1

Statement 2 alone is not sufficient

(C): Statement 1 and 2 combined are sufficient because x must equal 1

I hope my answer is right

Greetings
Max
Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 995
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 24 Apr 2017, 11:00
1
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Statement 2:
x²=1

x could either be 1 or -1

Statement 2 alone is not sufficient

(C): Statement 1 and 2 combined are sufficient because x must equal 1

I hope my answer is right

Greetings
Max



hi Wereheretotakeover

your solution is not correct

Ans is A

try again :)
Intern
Intern
avatar
Joined: 20 Apr 2017
Posts: 4
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 24 Apr 2017, 14:07
Mo2men wrote:
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7


Hi Max,

When you deal with such statement, you need to add extra step. You need to check the solutions you get in the original equation.

x =-7, substitute in original equation: |2x − 1| = 3x + 6

|-14 − 1| = -21 + 6......15=-15.........so, x=-7 is not viable solution.

x=-1
|- 3| = 3........3=3..............so x=-1 is viable solution

So we have only one answer.


Hi,

thank you very much! Completely forgot about it.

Greetings
Max
Intern
Intern
avatar
B
Joined: 09 Apr 2017
Posts: 8
GMAT ToolKit User
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 24 Apr 2017, 22:39
rohit8865 wrote:
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Statement 2:
x²=1

x could either be 1 or -1

Statement 2 alone is not sufficient

(C): Statement 1 and 2 combined are sufficient because x must equal 1

I hope my answer is right

Greetings
Max



hi Wereheretotakeover

your solution is not correct

Ans is A

try again :)


Answer should be D.

Statement 2 gives us 2 values for x: 1 & -1

Following the same method used for Statement 1, x = 1 does not give us a solution. Hence, -1 is the solution.
Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 995
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 24 Apr 2017, 22:46
koolhunk wrote:
rohit8865 wrote:
Wereheretotakeover wrote:
Hi,

please correct me if I'm wrong.

Statement 1:
|2x − 1| = 3x + 6

equals:
2x-1 = 3x+6
x=-7

2x-1 = -(3x+6)
x=1

Statement 1 alone is not sufficient because x could either be 1 or -7

Statement 2:
x²=1

x could either be 1 or -1

Statement 2 alone is not sufficient

(C): Statement 1 and 2 combined are sufficient because x must equal 1

I hope my answer is right

Greetings
Max



hi Wereheretotakeover

your solution is not correct

Ans is A

try again :)


Answer should be D.

Statement 2 gives us 2 values for x: 1 & -1

Following the same method used for Statement 1, x = 1 does not give us a solution. Hence, -1 is the solution.



i think u got confused over what question asked!!!!!!

Happy learning..........
Manager
Manager
avatar
S
Joined: 17 Aug 2012
Posts: 135
Location: India
Concentration: General Management, Strategy
Schools: Copenhagen, ESMT"19
GPA: 3.75
WE: Consulting (Energy and Utilities)
GMAT ToolKit User
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 25 Apr 2017, 09:04
statement 1 :|2x − 1| = 3x + 6
For X> 1/2 ; 2X-1 =3X + 6
X= -7 BUT X>1/2 hence not possible
For X<1/2 ; 2X-1 = -3X - 6
X=-1 OK
Only one solution

Statement 2 : two value of x hence no solution

Answer A
Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 749
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 01 Sep 2017, 19:14
Bunuel wrote:
What is the value of x?

(1) |2x − 1| = 3x + 6
(2) x^2 = 1


Have to be careful with the algebra here

Stmnt 1

2x- 1 = 3x + 6
-1= x + 6
x = -7


-l2x -1l = 3x + 6
-2x + 1 = 3x +6
1= 5x +6
-5 =5x
x = -1

Be careful- only negative one satisfies the equation so x= -7 cannot be a value of X

Suff

Stmnt 2

X^2= 1
x= -1 , 1

Insuff

A
BSchool Forum Moderator
avatar
P
Joined: 05 Jul 2017
Posts: 489
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
CAT Tests
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 08 Sep 2017, 22:33
Hey Bunuel

I need some help. I'm going wrong somewhere but I can't identify where. Below are the steps :-
(I'm trying to follow the same steps you used here in this post https://gmatclub.com/forum/what-is-x-12 ... l#p1037498)

Statement I: -
|2x − 1| = 3x + 6
LHS is non-negative, therefore RHS should alos be non-negative

3x+6>=0
x>= -2

2x − 1 = 3x + 6
Solving the above equation, we get
x= -7
We should discard this value as -7 < -2. For RHS to be positive we need something >= -2

How do I proceed ahead after this step? I want to use the conceptual method you used in the post I mentioned above. Please help. Thanks
_________________

My journey From 410 to 700 :-)
Here's my experience when I faced a glitch in my GMAT Exam
Don't do this mistake when you give your GMATPrep Mock!
NEW GMATPrep software analysis by Bunuel

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50000
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 08 Sep 2017, 22:42
1
pikolo2510 wrote:
Hey Bunuel

I need some help. I'm going wrong somewhere but I can't identify where. Below are the steps :-
(I'm trying to follow the same steps you used here in this post https://gmatclub.com/forum/what-is-x-12 ... l#p1037498)

Statement I: -
|2x − 1| = 3x + 6
LHS is non-negative, therefore RHS should alos be non-negative

3x+6>=0
x>= -2

2x − 1 = 3x + 6
Solving the above equation, we get
x= -7
We should discard this value as -7 < -2. For RHS to be positive we need something >= -2

How do I proceed ahead after this step? I want to use the conceptual method you used in the post I mentioned above. Please help. Thanks


You cannot use this method here becasue not for all values of x which are >= -2, the expression in the modulus (2x − 1) is positive.

In the problem you refer to we have |x| = 3x – 2. RHS must be >= 0, so x >= 2/3. Now, if x >= 2/3, then |x| = x, so we can write x = 3x - 2, which is not the case for the problem above.
_________________

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

BSchool Forum Moderator
avatar
P
Joined: 05 Jul 2017
Posts: 489
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
CAT Tests
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 09 Sep 2017, 11:56
Bunuel wrote:
pikolo2510 wrote:
Hey Bunuel

I need some help. I'm going wrong somewhere but I can't identify where. Below are the steps :-
(I'm trying to follow the same steps you used here in this post https://gmatclub.com/forum/what-is-x-12 ... l#p1037498)

Statement I: -
|2x − 1| = 3x + 6
LHS is non-negative, therefore RHS should alos be non-negative

3x+6>=0
x>= -2

2x − 1 = 3x + 6
Solving the above equation, we get
x= -7
We should discard this value as -7 < -2. For RHS to be positive we need something >= -2

How do I proceed ahead after this step? I want to use the conceptual method you used in the post I mentioned above. Please help. Thanks


You cannot use this method here becasue not for all values of x which are >= -2, the expression in the modulus (2x − 1) is positive.

In the problem you refer to we have |x| = 3x – 2. RHS must be >= 0, so x >= 2/3. Now, if x >= 2/3, then |x| = x, so we can write x = 3x - 2, which is not the case for the problem above.


Got it, Thanks a ton Bunuel!
_________________

My journey From 410 to 700 :-)
Here's my experience when I faced a glitch in my GMAT Exam
Don't do this mistake when you give your GMATPrep Mock!
NEW GMATPrep software analysis by Bunuel

Manager
Manager
avatar
B
Joined: 24 Sep 2018
Posts: 113
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1  [#permalink]

Show Tags

New post 25 Sep 2018, 13:24
For the first statement you need to use the two case approach for absolute values.

|2x−1|=3x+6 means that: 3x+6 could equal 2x−1, in which case:
x=−7
or, 3x+6 could equal −(2x−1) in which case:
3x+6=−2x+1, so
5x=−5
and therefore:

x=−1
So with two possible values it would be very tempting to say that statement 1 is not sufficient, then recognize that while statement 2 is clearly not sufficient on its own, it eliminates x=−7as a possibility when you use the two statements together. But wait!

If you return to your work from statement 1 to plug your solutions back in for a quick logic test, you'll see that −7 is an extraneous solution: |2(−7)−1|=3(−7)+6
means that:

|−15|=−15

Which does not work, since the absolute value on the left means that the left-hand side will be POSITIVE 15, while the right is stuck at NEGATIVE 15. This is known as an extraneous solution, and is why the process for solving absolute values always includes the step "plug your solutions back into the equation to verify that they are valid." Here, since −7 is invalid, statement 1 guarantees that x=−1 is the sole solution, and statement 1 is therefore sufficient. The correct answer is A.
_________________

Please award :thumbup: kudos, If this post helped you in someway. :student_man:

GMAT Club Bot
Re: What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 1 &nbs [#permalink] 25 Sep 2018, 13:24
Display posts from previous: Sort by

What is the value of x? (1) |2x − 1| = 3x + 6 (2) x^2 = 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®.