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

It is currently 24 Sep 2018, 12:30


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.

for You

we will pick new questions that match your level based on your Timer History

Your Progress

every week, we’ll send you an estimated GMAT score based on your performance


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.


Request Expert Reply

Confirm Cancel

What is x?

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 18 Jun 2016
Posts: 266
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
GMAT ToolKit User Reviews Badge
Re: What is x?  [#permalink]

Show Tags

New post 31 Aug 2016, 14:26
Donnie84 wrote:
St1: |x| < 2

This implies that -2 < x < 2.

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.

Answer (B).

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 -

My CR notes -

Joined: 12 Nov 2016
Posts: 758
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

New post 01 Sep 2017, 20:49
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

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

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

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

Math Revolution GMAT Instructor
User avatar
Joined: 16 Aug 2015
Posts: 6239
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: What is x?  [#permalink]

Show Tags

New post 03 Sep 2017, 17:35
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.


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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

User avatar
Status: Target 760
Joined: 20 Aug 2014
Posts: 58
Location: India
Concentration: Strategy, Economics
GMAT 1: 670 Q50 V30
GPA: 3.25
WE: Corporate Finance (Investment Banking)
Reviews Badge CAT Tests
Re: What is x?  [#permalink]

Show Tags

New post 10 Nov 2017, 21:29
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.

Answer is B
User avatar
Joined: 15 May 2010
Posts: 170
Location: India
Concentration: Strategy, General Management
WE: Engineering (Manufacturing)
Reviews Badge
Re: What is x?  [#permalink]

Show Tags

New post 10 Nov 2017, 23:14

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
GMAT Club Bot
Re: What is x? &nbs [#permalink] 10 Nov 2017, 23:14

Go to page   Previous    1   2   [ 25 posts ] 

Display posts from previous: Sort by

What is x?

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

Events & Promotions



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®.