GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 03 Mar 2021, 10:48
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
What is the product of all possible solutions of the equation |x + 2|^
10 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 72292
CAT Tests Top Member of the Month
What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  25 Oct 2018, 02:31
36
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

78% (01:52) correct 22% (02:18) wrong based on 508 sessions

Hide Show timer Statistics

What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Most Helpful Expert Reply
User avatar
V
VeritasKarishma
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 11482
Location: Pune, India
Top Member of the Month
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  25 Oct 2018, 21:55
8
Kudos
8
Bookmarks
Expert Reply
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20


We always say that you need to keep an eye on the options from the beginning. Here, I see an equation with absolute values and we are looking for its solutions.
The product of the solutions look like easy numbers (I think -4, 5 etc).
I notice 0 and the first thing I do here is check for 0. Does x = 0 work? If yes, the product will be 0 no matter what the other values of x are.
x = 0 works!
We are done.

Answer (D)
_________________
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 >
Signature Read More
User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 72292
CAT Tests Top Member of the Month
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  04 Jul 2019, 05:22
1
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20


OFFICIAL EXPLANATION:




What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?


A. -20
B. -5
C. -4
D. 0
E. 20


Denote \(|x+2|\) as \(a\)

We get \(a^2 - 5a = -6\)

Solving quadratics gives \(a =3\) or \(a=2\)

Thus, \(|x+2|=3\) or \(|x+2|=2\)

Further solving gives, \(x=1\), \(x=-5\), \(x=0\), or \(x=-4\).

The product of those values is 0.


Answer: D
_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
User avatar
V
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 4956
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE:Education (Education)
Reviews Badge
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  25 Oct 2018, 03:43
1
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20


Let, \(|x + 2| = a\)

i.e. equation \(|x + 2|^2 - 5|x + 2| = -6\) becomes \(a^2 - 5a = -6\)

i.e. \(a^2 - 5a +6 = 0\)

i.e. \(a = 3, 2\)

If \(a = 3 = |x + 2|\) then \(x = 1 or -5\)

If \(a = 2 = |x + 2|\) then \(x = 0 or -4\)

Product of all possible values of \(x = (1)*(-5)*(0)*(-4) = 0\)

Answer: Option D
_________________
GMATinsight
Great Results (Q≥50 and V≥40) l Honest and Effective Admission Support l 100% Satisfaction !!!
One-on-One GMAT Skype classes l On-demand Quant Courses and Pricing l Admissions Consulting
Call/mail: +91-9999687183 l bhoopendra.singh@gmatinsight.com (for FREE Demo class/consultation)
SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE Resources: 22 FULL LENGTH TESTS l OG QUANT 50 Qn+VIDEO Sol. l NEW:QUANT REVISION Topicwise Quiz
Signature Read More
avatar
B
Euphor1a
Intern
Intern
Joined: 05 Sep 2018
Posts: 6
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  25 Oct 2018, 19:47
GMATinsight wrote:
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20


Let, \(|x + 2| = a\)

i.e. equation \(|x + 2|^2 - 5|x + 2| = -6\) becomes \(a^2 - 5a = -6\)

i.e. \(a^2 - 5a +6 = 0\)

i.e. \(a = 3, 2\)

If \(a = 3 = |x + 2|\) then \(x = 1 or -5\)

If \(a = 2 = |x + 2|\) then \(x = 0 or -4\)

Product of all possible values of \(x = (1)*(-5)*(0)*(-4) = 0\)

Answer: Option D


Hey Insight,

Hope you're well.

In a question like this, why can't I multiply out the brackets to make a quadratic equation then solve for x? For example, once I multiplied and simplified the above, I deduced: x^2 + 4x - 5 = 0, where x = -5 or 1. Therefore, the answer would be -5.

May you point out the flaw in my reasoning please?

Thanks in advance.
User avatar
V
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 4956
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE:Education (Education)
Reviews Badge
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  25 Oct 2018, 21:22
1
Kudos
Expert Reply
Euphor1a wrote:
GMATinsight wrote:
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20


Let, \(|x + 2| = a\)

i.e. equation \(|x + 2|^2 - 5|x + 2| = -6\) becomes \(a^2 - 5a = -6\)

i.e. \(a^2 - 5a +6 = 0\)

i.e. \(a = 3, 2\)

If \(a = 3 = |x + 2|\) then \(x = 1 or -5\)

If \(a = 2 = |x + 2|\) then \(x = 0 or -4\)

Product of all possible values of \(x = (1)*(-5)*(0)*(-4) = 0\)

Answer: Option D


Hey Insight,

Hope you're well.

In a question like this, why can't I multiply out the brackets to make a quadratic equation then solve for x? For example, once I multiplied and simplified the above, I deduced: x^2 + 4x - 5 = 0, where x = -5 or 1. Therefore, the answer would be -5.

May you point out the flaw in my reasoning please?

Thanks in advance.


It's not bracket (parenthesis) it's modulus sign which considers absolute value i.e. the part inside may be positive as well as negative. You have skipped the possibility of the x+2 to be negative when you treat it like a bracket.
_________________
GMATinsight
Great Results (Q≥50 and V≥40) l Honest and Effective Admission Support l 100% Satisfaction !!!
One-on-One GMAT Skype classes l On-demand Quant Courses and Pricing l Admissions Consulting
Call/mail: +91-9999687183 l bhoopendra.singh@gmatinsight.com (for FREE Demo class/consultation)
SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE Resources: 22 FULL LENGTH TESTS l OG QUANT 50 Qn+VIDEO Sol. l NEW:QUANT REVISION Topicwise Quiz
Signature Read More
User avatar
V
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 6940
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member Reviews Badge
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  26 Oct 2018, 23:00
What is the product of all possible solutions of the equation |x+2|2−5|x+2|=−6|x+2|2−5|x+2|=−6?

A. -20
B. -5
C. -4
D. 0
E. 20

Let |x+2|= Y
y^2-5y+6=0

solve for y = 2,3

since |x+2|= Y
we get values, 0,1,2,3
product would be 0 hence D
User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 72292
CAT Tests Top Member of the Month
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  24 Dec 2018, 03:40
Expert Reply
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20


Par of GMAT CLUB'S New Year's Quantitative Challenge Set


_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
avatar
D
exc4libur
SVP
SVP
Joined: 24 Nov 2016
Posts: 1894
Location: United States
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  07 Nov 2019, 12:46
1
Bookmarks
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20


\(|x + 2|^2 - 5|x + 2| = -6…x^2+4+4x-5|x+2|=-6…x^2+10+4x-5|x+2|=0\)

\(if:x+2>0…x>-2…then:|x+2|=positive\)
\(x^2+10+4x-5|x+2|=0…x^2+10+4x-5x-10=0…x^2-x=0…x(x-1)=0\)
\(since:x>-2…then:x=(0,1)=valid.solutions\)

\(if:x+2<0…x<-2…then:|x+2|=negative\)
\(x^2+10+4x-5|x+2|=0…x^2+10+4x-5(-x-2)=0…x^2+9x+20=0…(x+4)(x+5)=0\)
\(since:x<-2…then:…x=(-4,-5)=valid.solutions\)

\(product(0,1,-4,-5)=0\)

Ans. (D)
avatar
G
CEdward
VP
VP
Joined: 11 Aug 2020
Posts: 1164
Re: What is the product of all possible solutions of the equation |x + 2|^ [#permalink] New post  24 Jan 2021, 21:36
VeritasKarishma wrote:
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?

A. -20
B. -5
C. -4
D. 0
E. 20


We always say that you need to keep an eye on the options from the beginning. Here, I see an equation with absolute values and we are looking for its solutions.
The product of the solutions look like easy numbers (I think -4, 5 etc).
I notice 0 and the first thing I do here is check for 0. Does x = 0 work? If yes, the product will be 0 no matter what the other values of x are.
x = 0 works!
We are done.

Answer (D)


So it looks like in this instance if you plug in 0, it works. But doing that presupposes that x = 0. Isn't the question asking what is the product of xy?

Actually...so x = 0 ... xy = 0.
_________________
"Do not pray for an easy life, pray for the strength to endure a difficult one." - Bruce Lee
Signature Read More
GMAT Club Bot
gmatclubot
[#permalink]
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
9514 posts
Bunuel
Math Expert
72285 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2417 posts
generis
Senior SC Moderator
4557 posts
Feedback

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions