NEW HERE? LEARN MORE
closeclose
It is currently 19 Apr 2024, 07:00
Register
GMAT Focus 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 sum of all possible solutions to |x - 3|^2 + |x - 3| = 20

9 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
B
Alex75PAris
Manager
Manager
Joined: 16 Mar 2016
Posts: 104
Location: France
Schools: Marshall '19 Darden '19 HKUST '19 Anderson '19
GMAT 1: 660 Q47 V33
GPA: 3.25
GMAT ToolKit User
What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink] New post  26 May 2016, 13:12
3
Kudos
36
Bookmarks
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

59% (02:03) correct 41% (02:32) wrong based on 479 sessions
Hide Show timer Statistics
What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 ?

A -1
B 6
C 7
D 12
E 14
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92760
CAT Tests Forum Quiz Mode
Re: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink] New post  26 May 2016, 13:28
4
Kudos
13
Bookmarks
Expert Reply
Alex75PAris wrote:
What is the sum of all possible solutions to |x - 3|² + |x - 3| = 20 ?

A -1
B 6
C 7
D 12
E 14


First of all |x - 3|^2 = (x - 3)^2, so we have: (x - 3)^2 + |x - 3| = 20.

When x < 3, x - 3 is negative, thus |x - 3| = -(x - 3). In this case we'll have (x - 3)^2 - (x - 3) = 20 --> x = -1 or x = 8. Discard x = 8 because it's not in the range we consider (< 3).

When x >= 3, x - 3 is non-negative, thus |x - 3| = x - 3. In this case we'll have (x - 3)^2 + (x - 3) = 20 --> x = -2 or x = 7. Discard x = -2 because it's not in the range we consider (>= 3).

Thus there are two solutions: x = -1 and x = 7 --> the sum = 6.

Answer: B.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92760
CAT Tests Forum Quiz Mode
Re: What is the sum of all possible solutions t [#permalink] New post  26 May 2016, 13:31
9
Kudos
2
Bookmarks
Expert Reply
Alex75PAris wrote:
What is the sum of all possible solutions to |x - 3|² + |x - 3| = 20 ?

A -1
B 6
C 7
D 12
E 14


Another way.

Denote |x - 3| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.

y = |x - 3| = 4 --> x = 7 or x = -1. The sum = 6.

Answer: B.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
User avatar
G
jfranciscocuencag
Manager
Manager
Joined: 12 Sep 2017
Posts: 239
What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink] New post  24 Dec 2018, 15:15
Bunuel wrote:
Alex75PAris wrote:
What is the sum of all possible solutions to |x - 3|² + |x - 3| = 20 ?

A -1
B 6
C 7
D 12
E 14


Another way.

Denote |x - 3| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.

y = |x - 3| = 4 --> x = 7 or x = -1. The sum = 6.

Answer: B.


Hello Bunuel!

Why is it -5 and 4?

Is not as the following?

a2 + a - 20 = 0

(a + 5 ) (a - 4 ) = 0

Best regards!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92760
CAT Tests Forum Quiz Mode
Re: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink] New post  24 Dec 2018, 20:15
Expert Reply
jfranciscocuencag wrote:
Bunuel wrote:
Alex75PAris wrote:
What is the sum of all possible solutions to |x - 3|² + |x - 3| = 20 ?

A -1
B 6
C 7
D 12
E 14


Another way.

Denote |x - 3| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.

y = |x - 3| = 4 --> x = 7 or x = -1. The sum = 6.

Answer: B.


Hello Bunuel!

Why is it -5 and 4?

Is not as the following?

a2 + a - 20 = 0

(a + 5 ) (a - 4 ) = 0

Best regards!


(y + 5 )(y - 4 ) = 0

y + 5 = 0 --> y = -5.
y - 4 = 0 --> y = 4.

P.S. Why are you using 'a' if there is 'y' in the solution?
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
P
eswarchethu135
Senior Manager
Senior Manager
Joined: 13 Jan 2018
Posts: 279
Location: India
Concentration: Operations, General Management
Schools: EDHEC Sept 2019 Intake (A) Erasmus '20 IE Jan20 Intake (A)
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE:Consulting (Consulting)
Reviews Badge
Re: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink] New post  24 Dec 2018, 21:51
3
Kudos
1
Bookmarks
\(|x - 3|^2 + |x - 3| = 20\)

Let |x-3| = a

\(a^2 + a - 20 = 0\)
\(a^2 + 5a - 4a - 20 = 0\)
\(a(a+5) - 4(a+5) = 0\)
\((a-4)(a+5)=0\)
\(a = 4, -5\)

As |x-3| = a, |x-3| = 4, -5. But modulus of any value cannot be a negative integer. So |x-3| = 4

x-3 = 4, -4
x = 7, -1

Sum of possible solutions is => 7-1 => 6

OPTION: B
avatar
B
Albs
Intern
Intern
Joined: 16 Nov 2015
Posts: 44
Location: United Kingdom
Concentration: Social Entrepreneurship, Other
Schools: Instead Sept 20 Intake (D) Imperial '22 (A) Oxford "21 (D) Cass '21 (A$) Cambridge "21
GMAT 1: 610 Q39 V35
Re: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink] New post  08 Feb 2019, 12:40
Sorry i still don't understand the following

(x - 3)^2 - (x - 3) = 20 --> x = -1 or x = 8.

isn't it (x-3)(x-3)-(x-3)=20
(x^2)-6x+9-x+3=20
(x^2)-7x+12=20
(x^2)-7x=8
Bunuel - how did you factorize it to get -1 and 8. Was it just by plugging numbers in?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92760
CAT Tests Forum Quiz Mode
Re: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink] New post  09 Feb 2019, 00:50
Expert Reply
Albs wrote:
Sorry i still don't understand the following

(x - 3)^2 - (x - 3) = 20 --> x = -1 or x = 8.

isn't it (x-3)(x-3)-(x-3)=20
(x^2)-6x+9-x+3=20
(x^2)-7x+12=20
(x^2)-7x=8
Bunuel - how did you factorize it to get -1 and 8. Was it just by plugging numbers in?


\((x - 3)^2 - (x - 3) = 20\)
\(x^2 - 6x + 9 - x + 3 = 20\)
\(x^2 - 7 x - 8 = 0\)

From here you can either factor to get (x - 4) (x - 3) = 20 or solve using discriminant.

Check the links below:

Factoring Quadratics
Solving Quadratic Equations


7. Algebra



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32542
Re: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink] New post  12 Jun 2023, 08:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 [#permalink]
12 Jun 2023, 08:47
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
92759 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

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