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

It is currently 20 Jun 2019, 00:21

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

If 25|x^2−5x−10|=100, then what is the sum of all the possible values

  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: 55715
If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 04 May 2016, 11:08
1
3
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (02:20) correct 20% (02:27) wrong based on 262 sessions

HideShow timer Statistics

Intern
Intern
User avatar
B
Joined: 14 Dec 2015
Posts: 46
Concentration: Entrepreneurship, General Management
WE: Information Technology (Computer Software)
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post Updated on: 04 May 2016, 12:09
It is 10.

|expression| = 4
exp = +4 => on solving x=7 and -2
exp = -4 => on solving x = 3 and 2
7 - 2 + 2 + 3 = 10

updated *roots for 2nd exp are wrong, that should be 6 or -1 instead of +3 or -2*

7-2+6-1 = 10 is correct


oa pls
_________________
"Fight the HARDEST battle that anyone can ever imagine"

Originally posted by snorkeler on 04 May 2016, 11:42.
Last edited by snorkeler on 04 May 2016, 12:09, edited 3 times in total.
Manager
Manager
avatar
Joined: 13 Apr 2016
Posts: 58
Location: India
GMAT 1: 640 Q50 V27
GPA: 3
WE: Operations (Hospitality and Tourism)
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 04 May 2016, 11:56
2
2
[quote="Bunuel"]If \(25|x^2−5x−10|=100\), then what is the sum of all the possible values of x?

A. 10
B. 8
C. 2
D. -4
E. -8

Answer is A

x^2-5x-10=4 will give you x=-2 and 7
-(x^2-5x-10)= 4 will give you x =-1 and 6
-2+7+-1+6=10
Manager
Manager
User avatar
B
Joined: 16 Mar 2016
Posts: 125
Location: France
GMAT 1: 660 Q47 V33
GPA: 3.25
GMAT ToolKit User
If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 04 May 2016, 13:49
3
x² - 5x - 10 = 4 => x² - 5x - 14 = 0 => (x - 7) (x + 2) = 0 => x = 7 or x = -2
x² - 5x - 10 = - 4 => x² - 5x - 6 = 0 => (x + 1) (x- 6) = 0 => x = 6 or x = -1

7 -2 + 6 - 1 = 10
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3893
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 31 Dec 2018, 04:51
Bunuel wrote:
If \(25|x^2−5x−10|=100\), then what is the sum of all the possible values of x?

A. 10
B. 8
C. 2
D. -4
E. -8



\(25|x^2−5x−10|=100\)

|x^2−5x−10|=4

x^2−5x−10=4
x=7 & -2
or say
-(x^2−5x−10)=4
x=3,+2

sum = 7-2+2+3 = 10

IMO A
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2892
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 02 Jan 2019, 05:18
1

Solution


Given:
    • \(25|x^2 - 5x - 10| = 100\)

To find:
    • The sum of all the possible values of x

Approach and Working:
\(|x^2 - 5x - 10| = \frac{100}{25}= 4\)
    • This implies, \(x^2 - 5x – 10 = 4\) or \(x^2 - 5x – 10 = -4\)
      o \(x^2 - 5x – 14 = 0\), implies, x = 7 or -2
      o \(x^2 - 5x – 6 = 0\), implies, x = 6 or -1

Therefore, sum of all possible values of x = 7 – 2 + 6 – 1 = 10

Hence, the correct answer is Option A

Answer: A

Image

_________________
VP
VP
avatar
G
Joined: 09 Mar 2018
Posts: 1003
Location: India
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 01 Feb 2019, 23:41
Bunuel wrote:
If \(25|x^2−5x−10|=100\), then what is the sum of all the possible values of x?

A. 10
B. 8
C. 2
D. -4
E. -8


Just solve both the quadratic expressions formed when we open the modulus

\(x^2 - 5x -14 = 0\), will give x as -2 and 7

\(x^2 - 5x + 6 = 0\), will give x as 2 and 3

Add all the values of x to get 10

A
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Intern
Intern
avatar
B
Joined: 02 Mar 2016
Posts: 2
Location: India
Concentration: Finance, Technology
GPA: 3.66
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 14 Feb 2019, 23:49
for the equation ax^2 + bx + c = 0 ,the sum of roots is given by (-b/a)

now acc. to ques:
|x^2−5x−10|=4

=> x^2−5x−10= 4 ...... eq(1)
and x^2−5x−10= -4 ...... eq(2)

now from eq (1) and eq (2)

r1 + r2 = -(-5/1)= 5
r3 + r4 = -(-5/1)= 5

therefore , r1 + r2 + r3 + r4= 10
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2942
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 15 Feb 2019, 00:33
Bunuel wrote:
If \(25|x^2−5x−10|=100\), then what is the sum of all the possible values of x?

A. 10
B. 8
C. 2
D. -4
E. -8


\(25|x^2−5x−10|=100\)

i.e. \(|x^2−5x−10|=4\)

i.e. \(x^2−5x−10=4\) or i.e. \(x^2−5x−10=-4\)

i.e. \(x^2−5x−14=0\) or i.e. \(x^2−5x−6=0\)

i.e. \(x^2−7x+2x−14=0\) or i.e. \(x^2−6x+x−6=0\)

i.e. \((x+2)*(x-7)=0\) or i.e. \((x−6)*(x+1)=0\)

i.e. x = -2, 7, 6, -1

Aum of all values of x = 10

Answer: Option A
_________________
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: 29 Apr 2018
Posts: 1
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values  [#permalink]

Show Tags

New post 29 Mar 2019, 11:43
hello folks!

if we apply the 'open up modulus' method, and find the solutions from both equations (i.e. 6, -1, 7, -2), do we need to test each one solution in the formula and check if they're correct?

or can we just take the solutions and sum them up without checking?

thanks!
GMAT Club Bot
Re: If 25|x^2−5x−10|=100, then what is the sum of all the possible values   [#permalink] 29 Mar 2019, 11:43
Display posts from previous: Sort by

If 25|x^2−5x−10|=100, then what is the sum of all the possible values

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


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