Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 16 Jun 2011
Posts: 19

If x = 3x  2, then x = ? [#permalink]
Show Tags
01 Oct 2011, 18:05
2
This post received KUDOS
21
This post was BOOKMARKED
Question Stats:
48% (00:45) correct 52% (00:38) wrong based on 1227 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!
Official Answer and Stats are available only to registered users. Register/ Login.



Director
Joined: 28 Jul 2011
Posts: 512
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, 19:04
Its Both 1 and 1/2 as x=3x2 It cab be x= 3x2 or x= (3x2) so when x= 3x2 we get x=1 when x=(3x2) we get x= 1/2 so It is both 1 and 1/2
_________________
+1 Kudos If found helpful..



Manager
Joined: 03 Mar 2011
Posts: 88
Location: United States
GPA: 3.9

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
01 Oct 2011, 23:09
19
This post received KUDOS
6
This post was BOOKMARKED
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: \(x=3x2\) \(x=3x2 , x>=0\) \(x=3x2, x<0\) \(2x=2, x>=0\) \(4x=2, x<0\) \(x=1, x>=0\) \(x=0.5, x<0\) 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!



Intern
Joined: 16 Jun 2011
Posts: 19

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
02 Oct 2011, 05:54
kotela wrote: Its Both 1 and 1/2
as x=3x2
It cab be x= 3x2 or x= (3x2) so
when x= 3x2 we get x=1 when x=(3x2) 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: 321

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
02 Oct 2011, 23:12
2
This post received KUDOS
1
This post was BOOKMARKED
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:
Last edited by pike on 03 Oct 2011, 00:47, edited 1 time in total.



Senior Manager
Joined: 23 Oct 2010
Posts: 375
Location: Azerbaijan
Concentration: Finance

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
02 Oct 2011, 23:33
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7951
Location: Pune, India

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
03 Oct 2011, 03:22
5
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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 My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 16 Jun 2011
Posts: 19

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
03 Oct 2011, 09:44
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: 18
Location: United States

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
03 Oct 2011, 18:35
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

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
03 Oct 2011, 20:41
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 3x2 negative. For 1/2, again 3x2 becomes negative. So only option left is (A).



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7951
Location: Pune, India

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
04 Oct 2011, 03:03
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 My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 10 Sep 2011
Posts: 12
Concentration: Finance, Strategy
GMAT Date: 12272011
GPA: 3.77
WE: Operations (Investment Banking)

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
06 Oct 2011, 02:53
Answer: A
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.



NonHuman User
Joined: 09 Sep 2013
Posts: 13804

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
18 Sep 2013, 06:23
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Joined: 10 Sep 2013
Posts: 80
Concentration: Sustainability, International Business

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
21 Sep 2013, 00:06
2
This post was BOOKMARKED
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: 152
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, 08:40
5
This post received KUDOS
2
This post was BOOKMARKED
Here is the sol. I have attached a screenshot. HTH
Attachments
image.jpg [ 506.41 KiB  Viewed 6443 times ]



Intern
Joined: 27 Mar 2014
Posts: 26

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
18 Jun 2014, 20:51
email2vm wrote: Here is the sol. I have attached a screenshot. HTH As (3x2)>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: 132
Concentration: Strategy, Entrepreneurship

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
30 Aug 2014, 08:30
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: 43867

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
01 Sep 2014, 00:26



Intern
Joined: 23 Dec 2014
Posts: 49

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
27 Dec 2014, 11:46
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: 43867

Re: If x = 3x  2, then x = ? [#permalink]
Show Tags
28 Dec 2014, 04:36




Re: If x = 3x  2, then x = ?
[#permalink]
28 Dec 2014, 04:36



Go to page
1 2
Next
[ 24 posts ]



