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

It is currently 15 Oct 2018, 18:59

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 sum of the solutions of the equation (x-1)^2=|x-1|?

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

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6362
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 26 Sep 2018, 05:06
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (00:56) correct 38% (01:19) wrong based on 146 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

What is the sum of the solutions of the equation \((x-1)^2=|x-1|?\)

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 2\)
\(E. 3\)

_________________

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"

Math Revolution Discount CodesJamboree Discount CodesVeritas Prep GMAT Discount Codes
Most Helpful Community Reply
Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 622
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post Updated on: 04 Oct 2018, 12:06
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the sum of the solutions of the equation \((x-1)^2=|x-1|?\)

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 2\)
\(E. 3\)


\((x-1)^2=|x-1|\)

For x>=1,
\(|x-1| = x-1\)
So, \((x-1)^2=x-1\)
(x-1)(x-2) = 0
x =1,2 (since both 1,2>=1 . so both solutions are valid)

for x<1,
\(|x-1| = -(x-1)\)
So, \((x-1)^2=-(x-1)\)
(x-1)(x) = 0
x =1,0 (since only 0<1. so 0 is a valid solution)

So valid solutions for x are 0,1,2
Sum of solutions = 3
\(E. 3\)
_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".


Originally posted by shashankism on 03 Oct 2018, 05:01.
Last edited by shashankism on 04 Oct 2018, 12:06, edited 1 time in total.
General Discussion
GMATH Teacher
User avatar
S
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 360
What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 26 Sep 2018, 05:52
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the sum of the solutions of the equation \((x-1)^2=|x-1|?\)

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 2\)
\(E. 3\)

\(?\,\,\,:\,\,\,{\text{sum}}\,\,{\text{of}}\,\,{\text{roots}}\)

\({\left( {x - 1} \right)^2} = \left| {x - 1} \right|\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{\left( {x - 1} \right)^4} = {\left( {x - 1} \right)^2}\,\,\,\,\, \Rightarrow \,\,\,\,\left\{ \begin{gathered}
\,\,\,x = 1\,\,\,\left( {{\text{trivial}}\,\,{\text{inspection}}} \right) \hfill \\
\,\,{\text{for}}\,\,x \ne 1\,\,:\,\,\,\,\,\frac{{{{\left( {x - 1} \right)}^4}}}{{{{\left( {x - 1} \right)}^2}}} = \frac{{{{\left( {x - 1} \right)}^2}}}{{{{\left( {x - 1} \right)}^2}}}\,\,\,\,\, \Rightarrow \,\,\,\,{\left( {x - 1} \right)^2} = 1\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 0\,\,\,{\text{or}}\,\,\,x = 2 \hfill \\
\end{gathered} \right.\)

(*) When we "square" one equation (or, in general, put it to an EVEN positive power), we don´t loose original roots, but we eventually "add" new ones.
That´s why, in the end, we must check each POTENTIAL root in the original equation! All of them fit here. Therefore:


\(? = 1 + 0 + 2 = 3\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6362
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 28 Sep 2018, 00:40
=>

\((x-1)^2=|x-1|\)
\(=> |x-1|^2=|x-1|\)
\(=> |x-1|^2-|x-1|=0\)
\(=> |x-1| (|x-1|-1)=0\)
\(=> |x-1| = 0\) or \(|x-1|-1=0\)
\(=> |x-1| = 0\) or \(|x-1|=1\)
\(=> x-1 = 0\) or \(x-1=±1\)
\(=> x=1 = 0\) or \(x=1±1\)
\(=> x=1, x=0\) or \(x=2\)

The sum of the solutions is \(0 + 1 + 2 = 3.\)

Therefore, the answer is E.
Answer: 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"

Intern
Intern
avatar
B
Joined: 28 Jun 2018
Posts: 21
Re: What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 29 Sep 2018, 07:29
chetan2u Is it wrong if I solve two equations separately and add??

These two:
1) (x-1)^2 = -(x-1)
2) (x-1)^2 = (x-1)

Because I am getting the answer right, but the values I am adding are not the same :/ I'm getting -1 + 1 + 3 =0

Please help! :(
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6958
Re: What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 29 Sep 2018, 09:59
hibobotamuss wrote:
chetan2u Is it wrong if I solve two equations separately and add??

These two:
1) (x-1)^2 = -(x-1)
2) (x-1)^2 = (x-1)

Because I am getting the answer right, but the values I am adding are not the same :/ I'm getting -1 + 1 + 3 =0

Please help! :(


-1 and 3 are wrong ..
(X-1)^2=-(x-1).......(x-1)(x-1+1)=0....(x-1)(x)=0, so x=0 or 1
(X-1)^2=x-1......(x-1)(x-1-1)=(x-1)*(x-2)=0...,so x=1 or 2
Different values 0,1 and 2...
Even with your method answer will be 0,1,2
Recheck your solution
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
avatar
B
Joined: 21 Jun 2017
Posts: 83
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 30 Sep 2018, 11:09
(x-1)^2 = some positive quantity
So, mod(x-1) will be positive or (x-1)will be positive

-----> (x-1)^2= x-1 or x=1 or 2 Sum = 1+2
Cheers !
_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Intern
Intern
avatar
B
Joined: 09 Apr 2018
Posts: 24
GPA: 4
What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 03 Oct 2018, 03:40
1
As for all absolute value questions, we have to consider 2 cases (>0 and <0).

Case 1
\((x-1)^2=(x-1)\)
(x-1)(x-1)=(x-1) | divide by (x-1)
(x-1)=1

x=2

Case 2
\((x-1)^2=-(x-1)\)
\((x-1)^2=-x+1)\)
\(x^2+1-2x=-x+1\)
\(x^2-x=0\)
\(x(x-1)=0\)

x=0, x=1

Sum = 2+1+0=3

Please hit Kudos if you liked this approach :)
Manager
Manager
avatar
B
Joined: 24 Dec 2017
Posts: 114
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 03 Oct 2018, 08:56
(x-1)^2 = |x-1|
=>x^2-2x+1 = |x-1|
=>x^2-3x+2 Solving it I got x=2 and x=1
=>Adding them, we get 2+1=3

Hence E but I am not sure if my method is correct. Can someone guide me please?

Thank you
Arjun
GMATH Teacher
User avatar
S
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 360
Re: What is the sum of the solutions of the equation (x-1)^2=|x-1|?  [#permalink]

Show Tags

New post 03 Oct 2018, 10:46
ArjunJag1328 wrote:
(x-1)^2 = |x-1|
=>x^2-2x+1 = |x-1|
=>x^2-3x+2 Solving it I got x=2 and x=1
=>Adding them, we get 2+1=3

Hence E but I am not sure if my method is correct. Can someone guide me please?

Thank you
Arjun

Hi, Arjun!

It´s not correct. Please look at shashankism´s perfect solution (above).
Reason: he started exactly like you. Then he (correctly) considered |x-1| in the two possible scenarios, to finish his solution"shielded".
(You did not find 0, did you realize that?)
Another thing, be careful not to transform an EQUATION into an EXPRESSION (in red). Expressions do not have "roots"!

Regards,
Fabio.
_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

GMAT Club Bot
Re: What is the sum of the solutions of the equation (x-1)^2=|x-1|? &nbs [#permalink] 03 Oct 2018, 10:46
Display posts from previous: Sort by

What is the sum of the solutions of the equation (x-1)^2=|x-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®.