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

It is currently 19 Nov 2018, 01:23

INSEAD R1 Results This Week!

First Decision Reported on Decision Tracker  |  Join INSEAD Chat to Calm Your Nerves & Catch the Latest Action


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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50658
If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 29 Apr 2016, 01:34
1
34
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

43% (02:15) correct 57% (02:32) wrong based on 469 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7037
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 29 Apr 2016, 09:06
3
2
Bunuel wrote:
If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?

A. 1
B. 3
C. 4
D. 5
E. 15


Hi,
A very good Q, which tells us to be very careful while dealing with MODULUS
Lets solve it by critical method to avoid any ERROR..



One critical point at x=1.. so TWO ranges


1) x<1..
\(x^2-5x+6=2-{-(x-1)}\)..
\(x^2-5x+6=2+x-1\)..
\(=> x^2-6x+5=0\) OR\(x^2-5x-x+5=0\) or \((x-5)(x-1)=0\)
x=5 or x=1..
BUT since we are looking at the range x<1, BOTH 1 and 5 are not valid..


2) x>=1
\(x^2-5x+6=2-(x-1)\)..
\(x^2-5x+6=2-x+1\)..
\(=> x^2-4x+3=0\) OR \(x^2-3x-x+3=0\) or\((x-3)(x-1)=0\)
x=3 or x=1..
As we are looking at the range x>=1, BOTH 3 and 1 are VALID solution..

so product =1*3=3
B
_________________

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

General Discussion
Intern
Intern
avatar
Joined: 14 Mar 2016
Posts: 3
Location: United States
Concentration: Technology, Strategy
Schools: Sloan '19
GPA: 3.2
WE: Business Development (Computer Software)
GMAT ToolKit User
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 29 Apr 2016, 08:39
1
I solved it by isolating the modulus from the rest of the equation and solving two different quadratic equations:
x-1 = xˆ2-5x+4 -> xˆ2-6x+5=0 -> x1 = 5, x2 = 1
x-1 = -xˆ2+5x-4 -> -xˆ2+4x-3=0 -> x1 = -1, x2 = -3

Solution: 3x5 = 15, letter E
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7037
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 29 Apr 2016, 08:56
2
3
marcelonac wrote:
I solved it by isolating the modulus from the rest of the equation and solving two different quadratic equations:
x-1 = xˆ2-5x+4 -> xˆ2-6x+5=0 -> x1 = 5, x2 = 1
x-1 = -xˆ2+5x-4 -> -xˆ2+4x-3=0 -> x1 = -1, x2 = -3

Solution: 3x5 = 15, letter E


Hi,

you have found the different values of x correctly as 5,1,3,1..
BUT which are the valid values- you will have to substitute and check- WHY?
Since you are dealing with MODULUS..

\(x^2−5x+6=2−|x−1|\)..

1)5 --
\(5^2-5*5+6=2-|5-1|\)..
\(25-25+6=2-4\) or \(6=-4\).. NO, so 5 is not valid..

2)1--
\(1^2-5*1+6=2-|1-1|\)..
\(2=2\).. VALID

3) 3 --
\(3^2-5*3+6=2-|3-1|\)..
\(9-15+6 = 2-2\) or \(0=0\).. VALID..

so there are two valid solutions 1 and 3..
ans 1*3 = 3
B
_________________

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

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4224
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 29 Apr 2016, 12:04
Bunuel wrote:
If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?

A. 1
B. 3
C. 4
D. 5
E. 15


Try substituting the values from the options

\(x^2−5x+6=2−|x−1|\)

Option (A)

\(1^2−5*1+6=2−|1−1|\)

\(1−5+6=2−|0|\)

\(10 not =2\)

Option (B)

\(3^2−5*3+6=2−|3−1|\)

\(9−5*3+6=2−2\)

\(15−15=2−2\)

Hence this is our answer , you don't need to go beyond that, to mark the answer as (B)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Manager
Manager
User avatar
B
Joined: 16 Mar 2016
Posts: 129
Location: France
GMAT 1: 660 Q47 V33
GPA: 3.25
GMAT ToolKit User
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 29 May 2016, 12:54
I don't understand ! :(

Here, we find the solutions : (1 or 5) for one case | x - 3| = x - 3
and (1 or 3) for the other case | x - 3| = - (x - 3) = - x + 3

This question teaches us that when we solve an equation with modulus, all the answers have to be double-checked ?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8560
Location: Pune, India
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 29 May 2016, 20:33
1
Abhishek009 wrote:
Bunuel wrote:
If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?

A. 1
B. 3
C. 4
D. 5
E. 15


Try substituting the values from the options

\(x^2−5x+6=2−|x−1|\)

Option (A)

\(1^2−5*1+6=2−|1−1|\)

\(1−5+6=2−|0|\)

\(10 not =2\)

Option (B)

\(3^2−5*3+6=2−|3−1|\)

\(9−5*3+6=2−2\)

\(15−15=2−2\)

Hence this is our answer , you don't need to go beyond that, to mark the answer as (B)


Yes, I would solve by substituting from the options too but note that I would not try option (A) at all and after option (B), I will need to try option (D) too.

Here are the reasons:
Option (A) is 1. If it satisfies, I am not able to eliminate any options because the product of the values of x would be the same whether you multiply by 1 or not. So no point trying out 1.

Option (B) needs to be tried out to find out whether 3 can be a value of x.

x^2−5x+6=2−|x−1|
3^2−5*3+6=2−|3−1|
0 = 0

So 3 is a value of x. Can we say answer must be (B) yet? No. You have 15 as an option too. So you must try 5 too. If that can also be the value of x, then the product will be 15 and answer will be (E).

5^2−5*5+6=2−|5−1|
6 is not equal to -2.
So 5 is not a value of x.

Now we can be sure that answer must be (B).
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

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

Senior Manager
Senior Manager
User avatar
Joined: 18 Jan 2010
Posts: 252
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 29 May 2016, 20:50
2
Bunuel wrote:
If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?

A. 1
B. 3
C. 4
D. 5
E. 15


Since modulus is given, it is prudent to solve this equation in two parts.

(1) x-1 > 0 or equal to 0. so x is greater than or equal to 1
Then |x−1| can be written as x-1.

The equation can be written as:

\(x^2\)−5x+6=2−(x−1)
\(x^2\)−5x+6=2−x+1
\(x^2\)−5x+6=3−x
\(x^2\)−4x+3=0
(x-1)(x-3) = 0 ; x = 1 or 3. This is in line with our assumption (that x is greater than or equal to 1)

(2) x-1 < 0. so x is less than 1
Then |x−1| can be written as -(x-1).

The equation can be written as:

\(x^2\)−5x+6=2−[-(x−1)]
\(x^2\)−5x+6=2+x-1
\(x^2\)−5x+6=1+x
\(x^2\)−6x+5=0
(x-1)(x-5) = 0; x = 1 or 5. This is NOT in line with our assumption (that x is less than 1)

Acceptable values: 1 and 3.

Product of these values: 1*3 = 3

B is the answer.
Manager
Manager
avatar
B
Joined: 29 Jul 2018
Posts: 90
Concentration: Finance, Statistics
GMAT ToolKit User CAT Tests
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?  [#permalink]

Show Tags

New post 31 Aug 2018, 16:03
case 1 x>=1
x^2-5x+6 = 2-x+1
x = 1,3(acceptable)
case 2 x<1
x^2-5x+6 = 2+x-1
x = 5,1 but x<1 so rejected
GMAT Club Bot
Re: If x^2−5x+6=2−|x−1|, what is the product of all possible values of x? &nbs [#permalink] 31 Aug 2018, 16:03
Display posts from previous: Sort by

If x^2−5x+6=2−|x−1|, what is the product of all possible values of x?

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


cron
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®.