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

 It is currently 18 Jan 2019, 20:20

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### 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.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# What is x?

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

### Hide Tags

Current Student
Joined: 18 Jun 2016
Posts: 264
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
Re: What is x?  [#permalink]

### Show Tags

31 Aug 2016, 13:26
Donnie84 wrote:
St1: |x| < 2

This implies that -2 < x < 2.
Insufficient.

St2: |x| = 3x – 2

Using one of Bunuel's legendary tricks:

Since absolute value is always >= 0, the expression on right hand side will be >= 0.

3x - 2 >= 0
x >= 2/3, meaning x is positive.

So, we can only check for one condition.

If x > 0

x = 3x - 2
2x = 2
x = 1 -> satisfies the condition that x is positive.
Sufficient.

The trick is legendary because it saves us from checking the condition x is negative. Let's see what will happen if we do check:

If x < 0

x = 2 - 3x
4x = 2
x = 1/2 -> does not satisfy the condition that x is negative.

As you can see, the trick saves time and can make a big difference in the actual exam.

Sorry to be critical but the trick IS NOT saving any time per say. If you follow the usual method, you have to check for 2 conditions - When |x| = +ve & when |x| = -ve. While in this method, we are first checking the range of values that x can take and then based upon it, we are calculating only when |x| = +ve. The number of check points is same in both the cases for This Particular question, but it may not be the case for any other question. We may get the range of x lying in both the quadrants in which case, Bunuel's method would ultimately lead to a longer solution.
_________________

I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html

Director
Joined: 12 Nov 2016
Posts: 731
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: What is x?  [#permalink]

### Show Tags

01 Sep 2017, 19:49
rohitgoel15 wrote:
What is x?

(1) |x| < 2
(2) |x| = 3x – 2

This question may be a C trap

Stmnt 1

X could be -1,0,1

Stmnt 2

Pos
x= 3x- 2
x +2 = 3x
2= 2x
x =1

Neg
-x= 3x-2
-x +2 =3x
2= 4x
x =1/2

1/2 does not satisfy the equation so x must be 1

B
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: What is x?  [#permalink]

### Show Tags

03 Sep 2017, 16:35
rohitgoel15 wrote:
What is x?

(1) |x| < 2
(2) |x| = 3x – 2

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Question

In the original condition, there is 1 variable $$x$$ and 0 equation. So you need 1 equation.

Condition 1)
Since it is an inequality, there is no equation. Thus we can't identify the variable x and this is not sufficient.

Condition 2)
i) $$x \ge 0$$
$$|x| = 3x - 2$$ is equivalent to $$x = 3x - 2$$ or $$2x - 2 = 0$$.
Thus we have $$x = 1$$.
This is sufficient.

ii) $$x < 0$$
$$|x| = 3x - 2$$ is equivalent to $$-x = 3x - 2$$ or $$4x - 2 = 0$$.
Thus we have $$x = 1/2$$. However $$x = 1/2 > 0$$.
There is no negative solution.

Therefore, we have a unique solution $$x = 1$$.
This condition is sufficient.

The answer is B.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Status: Target 760
Joined: 20 Aug 2014
Posts: 50
Location: India
Concentration: Strategy, Economics
GMAT 1: 730 Q49 V40
GPA: 3.6
WE: Corporate Finance (Consulting)
Re: What is x?  [#permalink]

### Show Tags

10 Nov 2017, 20:29
rohitgoel15 wrote:
What is x?

(1) |x| < 2
(2) |x| = 3x – 2

No where it is given that X is an integer. Hence, x can be any number between 0 and 2 by statement1.
From statement 2, we know that x is either 1 or 1/2. If 1/2, then the overall equation becomes negative and modulus can't be negative.

Manager
Joined: 15 May 2010
Posts: 159
Location: India
Concentration: Strategy, General Management
WE: Engineering (Manufacturing)
Re: What is x?  [#permalink]

### Show Tags

10 Nov 2017, 22:14
So,

A. |x|<2 meant

-2<x<2 leading to x= 0,1,-1,-0.5,-1.5

B. |x|=3x-2

|x| is positive.

So, unique value.

Sent from my iPhone using GMAT Club Forum
Non-Human User
Joined: 09 Sep 2013
Posts: 9432
Re: What is x?  [#permalink]

### Show Tags

13 Nov 2018, 09:47
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.
_________________
Re: What is x? &nbs [#permalink] 13 Nov 2018, 09:47

Go to page   Previous    1   2   [ 26 posts ]

Display posts from previous: Sort by

# What is x?

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

 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®.