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

 It is currently 17 Aug 2018, 06:10

### 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

# If |x| = 3x - 2, then x = ?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 Jun 2011
Posts: 19
If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

01 Oct 2011, 19:05
5
20
00:00

Difficulty:

45% (medium)

Question Stats:

50% (00:46) correct 50% (00:38) wrong based on 1159 sessions

### HideShow timer Statistics

If |x| = 3x - 2, then x = ?

A. 1
B. 1/2
C. 1 and 1/2
D. -1/2
E. -1

Soln
When we proceed to solve this we get two eq:
x = 3x - 2 .... (i) when x > 0
-x = 3x - 2 .... (ii) when x < 0

Therefore we get two results x = 1 and x = 1/2 from (i) and (ii) resp.
Lets plug the values back into the eq.

|1| = 3*1 - 2
==> 1 = 1
so (i) holds good.

|1/2| = 3*(1/2) - 2
==> 1/2 = -1/2 this is incorrect, hence soln from eq (ii) does not hold good.

The soln to the eq |x| = 3x - 2 is 1 only.

Quant guru's let me know if there is a flaw in my calculation method.

Thanks!
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8188
Location: Pune, India
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

03 Oct 2011, 04:22
6
1
2
mave23 wrote:
Hi All,

Came across this rather interesting quant question, and thought of sharing it with folks here:

|x| = 3x - 2

a. 1
b. 1/2
c. 1 and 1/2
d. -1/2
e. -1

I know it's fun to solve when you know what you are doing (and more importantly, why you are doing it) and the graph method is especially satisfying but don't forget a very basic trick in such questions. When you have values for x in the options, and an equation in the question, we could just plug the values in. Since x = 1 satisfies the equation and x = 1/2 doesn't, answer has to be (A).
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! ##### Most Helpful Community Reply Manager Joined: 03 Mar 2011 Posts: 88 Location: United States Schools: Erasmus (S) GMAT 1: 730 Q51 V37 GPA: 3.9 Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags 02 Oct 2011, 00:09 22 6 There is no big flaws, but it is not fully mathematically correct. When opening the absolute value you should add constraints which you use. In other words, $$|x|=x$$ if $$x>=0$$ So, the precise solution is as follows: $$|x|=3x-2$$ $$x=3x-2 , x>=0$$ $$-x=3x-2, x<0$$ $$2x=2, x>=0$$ $$4x=2, x<0$$ $$x=1, x>=0$$ $$x=0.5, x<0$$ So, the only answer is x=1. Good luck! Try to solve some more problems with absolute values (both equations and inequalities) _________________ If my post is useful for you not be ashamed to KUDO me! Let kudo each other! ##### General Discussion Senior Manager Joined: 28 Jul 2011 Posts: 404 Location: United States Concentration: International Business, General Management GPA: 3.86 WE: Accounting (Commercial Banking) Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags 01 Oct 2011, 20:04 Its Both 1 and 1/2 as |x|=3x-2 It cab be x= 3x-2 or x= -(3x-2) so when x= 3x-2 we get x=1 when x=-(3x-2) we get x= 1/2 so It is both 1 and 1/2 _________________ +1 Kudos If found helpful.. Intern Joined: 16 Jun 2011 Posts: 19 Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags 02 Oct 2011, 06:54 kotela wrote: Its Both 1 and 1/2 as |x|=3x-2 It cab be x= 3x-2 or x= -(3x-2) so when x= 3x-2 we get x=1 when x=-(3x-2) we get x= 1/2 so It is both 1 and 1/2 No x = 1/2 is not the solution, i have proved it, you can also read the message below yours, it too proves the same thing.. Current Student Joined: 08 Jan 2009 Posts: 309 GMAT 1: 770 Q50 V46 Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags Updated on: 03 Oct 2011, 01:47 2 1 I think one other point is that visually we should know this has only one solution. Visualize y = |x| Visualize y = 3x - 2 These will only intersect once! On the other hand, consider: |2x – 3| – 4 = 3 |2x – 3| = 7 We can see straight away this has two solutions. Visualize the left hand side and the right hand side: Originally posted by pike on 03 Oct 2011, 00:12. Last edited by pike on 03 Oct 2011, 01:47, edited 1 time in total. Senior Manager Joined: 23 Oct 2010 Posts: 361 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags 03 Oct 2011, 00:33 silly me . i have answered C. I must be burned and buried deeply for such a stupid mistake hehe _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth Intern Joined: 16 Jun 2011 Posts: 19 Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags 03 Oct 2011, 10:44 VeritasPrepKarishma wrote: I know it's fun to solve when you know what you are doing (and more importantly, why you are doing it) and the graph method is especially satisfying but don't forget a very basic trick in such questions. When you have values for x in the options, and an equation in the question, we could just plug the values in. Since x = 1 satisfies the equation and x = 1/2 doesn't, answer has to be (A). Wow thanks, you are correct i had overlooked this option.. do you think such questions will come in the real gmat, where plugging the value may reveal the answer? Thanks. Intern Joined: 26 May 2011 Posts: 15 Location: United States Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags 03 Oct 2011, 19:35 mave23 wrote: VeritasPrepKarishma wrote: I know it's fun to solve when you know what you are doing (and more importantly, why you are doing it) and the graph method is especially satisfying but don't forget a very basic trick in such questions. When you have values for x in the options, and an equation in the question, we could just plug the values in. Since x = 1 satisfies the equation and x = 1/2 doesn't, answer has to be (A). Wow thanks, you are correct i had overlooked this option.. do you think such questions will come in the real gmat, where plugging the value may reveal the answer? Thanks. depends on how you are doing in the exam Intern Joined: 10 May 2011 Posts: 22 Location: India Concentration: Strategy, General Management GMAT 1: 690 Q50 V32 Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags 03 Oct 2011, 21:41 Just another simple approach. Since |x| is always positive so 3x - 2 should always be positive for this equation to be true. You can simply rule out options (D) and (E), as any negative values of x will make 3x-2 negative. For 1/2, again 3x-2 becomes negative. So only option left is (A). Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8188 Location: Pune, India Re: If |x| = 3x - 2, then x = ? [#permalink] ### Show Tags 04 Oct 2011, 04:03 mave23 wrote: Wow thanks, you are correct i had overlooked this option.. do you think such questions will come in the real gmat, where plugging the value may reveal the answer? Thanks. Sure it is possible. That is why it is good to keep this in mind since a relatively tricky question can be easily solved this way. Though, GMAC is wise to such tricks and since these questions don't involve much work on your part, don't expect the options to help you often (nevertheless, you should always keep one eye on the options), at least not right in the beginning. If you do get such a question, it may not be a very high level question. _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Joined: 10 Sep 2011
Posts: 12
Concentration: Finance, Strategy
GMAT Date: 12-27-2011
GPA: 3.77
WE: Operations (Investment Banking)
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

06 Oct 2011, 03:53

Approach:
Substituted option A i.e x=1. Inequality satisfied.

This eliminates all options except option C. This is because only Option A & C carries x=1 which satisfies the inequality.

Substituted x=1/2. Inequality not satisfied. Hence Option C eliminated. Only remaining option A.
Selected Option A.

----------------------------------------------
P.S. - Thanks pike for the graphical solution. I loved your approach.
Manager
Joined: 10 Sep 2013
Posts: 79
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

21 Sep 2013, 01:06
2
Absolute values are easy. The hard part is remembering to substitute back into the original question to check if it satisfies the equation.

Here are some rules:
|x|>=0
|x| = sqrt(x)^2
|0| = 0
|-x|=|x|
|x|+|y|>= |x+y|

Absolute values can also be thought of as the distance between 2 points.

Remember to always always always check whether your solution satisfies the equation!!
_________________

Kudos if I helped

Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 146
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

26 Mar 2014, 09:40
5
1
Here is the sol. I have attached a screenshot. HTH
Attachments

image.jpg [ 506.41 KiB | Viewed 7203 times ]

Intern
Joined: 27 Mar 2014
Posts: 24
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

18 Jun 2014, 21:51
email2vm wrote:
Here is the sol. I have attached a screenshot. HTH

As (3x-2)>0, x>2/3>0, then we do not need to consider the case x<0. Reduce the amount of caculation.
Manager
Joined: 13 Oct 2013
Posts: 131
Concentration: Strategy, Entrepreneurship
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

30 Aug 2014, 09:30
so what is the question here? I am not able to see it. is it to find value of X?

mave23 wrote:
|x| = 3x - 2

A. 1
B. 1/2
C. 1 and 1/2
D. -1/2
E. -1

Soln
When we proceed to solve this we get two eq:
x = 3x - 2 .... (i) when x > 0
-x = 3x - 2 .... (ii) when x < 0

Therefore we get two results x = 1 and x = 1/2 from (i) and (ii) resp.
Lets plug the values back into the eq.

|1| = 3*1 - 2
==> 1 = 1
so (i) holds good.

|1/2| = 3*(1/2) - 2
==> 1/2 = -1/2 this is incorrect, hence soln from eq (ii) does not hold good.

The soln to the eq |x| = 3x - 2 is 1 only.

Quant guru's let me know if there is a flaw in my calculation method.

Thanks!

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way

Math Expert
Joined: 02 Sep 2009
Posts: 47967
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

01 Sep 2014, 01:26
sunita123 wrote:
so what is the question here? I am not able to see it. is it to find value of X?

mave23 wrote:
|x| = 3x - 2

A. 1
B. 1/2
C. 1 and 1/2
D. -1/2
E. -1

Soln
When we proceed to solve this we get two eq:
x = 3x - 2 .... (i) when x > 0
-x = 3x - 2 .... (ii) when x < 0

Therefore we get two results x = 1 and x = 1/2 from (i) and (ii) resp.
Lets plug the values back into the eq.

|1| = 3*1 - 2
==> 1 = 1
so (i) holds good.

|1/2| = 3*(1/2) - 2
==> 1/2 = -1/2 this is incorrect, hence soln from eq (ii) does not hold good.

The soln to the eq |x| = 3x - 2 is 1 only.

Quant guru's let me know if there is a flaw in my calculation method.

Thanks!

Edited the stem. Thank you.
_________________
Intern
Joined: 23 Dec 2014
Posts: 48
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

27 Dec 2014, 12:46
email2vm wrote:
Here is the sol. I have attached a screenshot. HTH

I also solved this way. is it right approach to solve this type of question?
Math Expert
Joined: 02 Sep 2009
Posts: 47967
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

28 Dec 2014, 05:36
Salvetor wrote:
email2vm wrote:
Here is the sol. I have attached a screenshot. HTH

I also solved this way. is it right approach to solve this type of question?

Yes, that approach is correct.
_________________
Board of Directors
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If |x| = 3x - 2, then x = ?  [#permalink]

### Show Tags

01 Feb 2016, 19:26
I agree, almost fell in the trap for 1/2
if we plug in 1/2, we then have 1/2 = 1.5-2, but the absolute value cannot be negative.
Re: If |x| = 3x - 2, then x = ? &nbs [#permalink] 01 Feb 2016, 19:26

Go to page    1   2    Next  [ 23 posts ]

Display posts from previous: Sort by

# Events & Promotions

 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®.