Find all School-related info fast with the new School-Specific MBA Forum

It is currently 04 May 2015, 04:27

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the product of all the solutions of x^2 - 4x + 6=3

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27201
Followers: 4225

Kudos [?]: 40975 [0], given: 5649

Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink] New post 06 Jul 2013, 08:53
Expert's post
jjack0310 wrote:
Bunuel wrote:
jjack0310 wrote:
Sorry. It is not clear.

Can you explain what was wrong with the way I was approaching the problem?

I mean other than the part that you marked red, what was I doing wrong? Do I have to solve theproblem using the solution that you mentioned?

If x > -2, how is |x + 2| = (x - 2)?
Is there an identity that I am missing?
If I plug in, X = -1, |x + 2| = 1, but (x - 2) = -3

Why the discrepancy? What identity am I missing?


There was a typo:
When \(x\leq{-2}\), then \(|x+2|=-(x+2)\)
When \(x>{-2}\), then \(|x+2|=(x+2)\).

Absolute value properties:

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\).

For our question, when x>-2 (when x+2>0), |x+2|=x+2.

Hope it's clear.


Got it.

Thanks,

Final question, why are there two possibilities for when x = 0? Is that correct? or a typo?


No, that's not a typo: |0|=0=-0.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 475
Followers: 1

Kudos [?]: 78 [0], given: 134

Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink] New post 09 Jul 2013, 14:25
What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1| ?
x^2 - 4x + 6 = 3 - |x - 1|
x^2 - 4x + 3 = - |x - 1|

x>1
x^2 - 4x + 6 = 3 - |x - 1|
x^2 - 4x + 3 = - (x-1)
x^2 - 4x + 3 = -x+1
x^2 - 3x +2 = 0
(x-1)(x-2)=0
x=1, x=2
2 falls within the range of x>1
x=2

x<1
x^2 - 4x + 6 = 3 - |x - 1|
x^2 - 4x + 6 = 3 - -(x-1)
x^2 - 4x + 6 = 3 - (-x+1)
x^2 - 4x + 3 = + x - 1
x^2 - 5x + 4 = 0
(x-1)(x-4) = 0
x=1, x=4
Neither 1 or 4 fall within the range of x<1
INVALID

The product is (2)

(C)

(Bunuel, could you explain to me how we know where the greater than or equals sign goes in these problems? I see that in your solution you had x>=1, but I don't know why that is as opposed to say, x<=1)

Thanks!
Intern
Intern
avatar
Joined: 27 Mar 2014
Posts: 26
Followers: 0

Kudos [?]: 11 [0], given: 12

Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink] New post 19 Jun 2014, 01:57
Bunuel wrote:
carcass wrote:
What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1| ?

(A) -8
(B) -4
(C) 2
(D) 4
(E) 8


If \(x<1\), then \(|x - 1| = -(x-1)=1-x\), so in this case we'll have \(x^2 - 4x + 6 = 3-(1-x)\) --> \(x^2-5x+4=0\) --> \(x=1\) or \(x=4\) --> discard both solutions since neither is in the range \(x<1\).

If \(x\geq{1}\), then \(|x - 1| = x-1\), so in this case we'll have \(x^2 - 4x + 6 = 3-(x-1)\) --> \(x^2-3x+2=0\) --> \(x=1\) or \(x=2\).

Therefore, the product of the roots is 1*2=2.

Answer: C.


Dear Bunuel,

We do not need to consider two situation of |x - 1|.

As, x^2 - 4x + 6 = 3 - |x - 1| <=> x^2 - 4x + 3 = - |x - 1| <0 => 1<x (<3) => x^2 - 4x + 3 = x-1 => x^2 - 5x + 4 = 0 => 2 solutions
Intern
Intern
avatar
Joined: 11 Sep 2014
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 1

Problem Solving Absolute Value [#permalink] New post 03 Nov 2014, 16:02
What is the product of all the solutions of (x^2) - (4x) + (6)= lx - 1l ?
a)-8
b)-4
c)-2
d)4
e)8

*Source: Total GMAT Math

My follow-up question is that since the absolute value will always be a positive number, can you automatically eliminate answer choices a, b, and c?

Thanks!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27201
Followers: 4225

Kudos [?]: 40975 [0], given: 5649

Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink] New post 04 Nov 2014, 02:49
Expert's post
ferlytate wrote:
What is the product of all the solutions of (x^2) - (4x) + (6)= lx - 1l ?
a)-8
b)-4
c)-2
d)4
e)8

*Source: Total GMAT Math

My follow-up question is that since the absolute value will always be a positive number, can you automatically eliminate answer choices a, b, and c?

Thanks!


Merging similar topics. Please refer to the discussion on page 1.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 3 and 5. Thank you.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Re: What is the product of all the solutions of x^2 - 4x + 6=3   [#permalink] 04 Nov 2014, 02:49

Go to page   Previous    1   2   [ 25 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic What is the product of all the solutions of x^2+4x+7=|x+2|+3? viktorija 7 21 Dec 2014, 20:17
9 Experts publish their posts in the topic 4^x + 4 ^-x = 2 What is the value of X nimc2012 18 07 Feb 2012, 08:56
product of all possible solutions mbaMission 8 02 Jun 2009, 03:59
What is the value of x? (1) x^4+x^2+1=(1/x^4+x^2+1) (2) Jamesk486 9 15 May 2007, 18:48
x^2 + 4x + 4/x + 1/x^2 + 5= 0 . What is the sum of the roots laxieqv 12 26 Apr 2006, 07:33
Display posts from previous: Sort by

What is the product of all the solutions of x^2 - 4x + 6=3

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.