Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 17 Jul 2019, 13:50

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 product of all possible solutions of the equation |x + 2|^

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56277
What is the product of all possible solutions of the equation |x + 2|^  [#permalink]

Show Tags

New post 25 Oct 2018, 03:31
15
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (01:47) correct 23% (02:23) wrong based on 231 sessions

HideShow timer Statistics


Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56277
Re: What is the product of all possible solutions of the equation |x + 2|^  [#permalink]

Show Tags

New post 04 Jul 2019, 06:22
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
_________________
General Discussion
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2959
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: What is the product of all possible solutions of the equation |x + 2|^  [#permalink]

Show Tags

New post 25 Oct 2018, 04:43
1
1
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
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Intern
avatar
B
Joined: 05 Sep 2018
Posts: 6
Re: What is the product of all possible solutions of the equation |x + 2|^  [#permalink]

Show Tags

New post 25 Oct 2018, 20:47
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.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2959
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: What is the product of all possible solutions of the equation |x + 2|^  [#permalink]

Show Tags

New post 25 Oct 2018, 22:22
1
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.
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9442
Location: Pune, India
Re: What is the product of all possible solutions of the equation |x + 2|^  [#permalink]

Show Tags

New post 25 Oct 2018, 22:55
3
1
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 >
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 4237
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: What is the product of all possible solutions of the equation |x + 2|^  [#permalink]

Show Tags

New post 27 Oct 2018, 00:00
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
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56277
Re: What is the product of all possible solutions of the equation |x + 2|^  [#permalink]

Show Tags

New post 24 Dec 2018, 04:40
GMAT Club Bot
Re: What is the product of all possible solutions of the equation |x + 2|^   [#permalink] 24 Dec 2018, 04:40
Display posts from previous: Sort by

What is the product of all possible solutions of the equation |x + 2|^

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





cron

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