GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 03 Aug 2020, 22:15

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

The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained

  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: 65771
The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 10 Mar 2020, 01:47
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:42) correct 39% (01:31) wrong based on 201 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator l A learner forever :)
Joined: 08 Jul 2010
Posts: 4511
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 10 Mar 2020, 03:17
2
Bunuel wrote:
The minimum value of \(f(x) = |10 – x| + |x – 2| – |4 – x|\) is attained at x = ?

A. 2
B. 4
C. 8
D. 10
E. 12


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions



Method 1

Substitute values of x from options

Answer: Option D


Method 2

Draw graph and check the value of x for which graph has min. value
Attachments

Screenshot 2020-03-10 at 4.45.54 PM.png
Screenshot 2020-03-10 at 4.45.54 PM.png [ 252.07 KiB | Viewed 1525 times ]


_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 3339
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Reviews Badge CAT Tests
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 10 Mar 2020, 01:55
1
Bunuel wrote:
The minimum value of \(f(x) = |10 – x| + |x – 2| – |4 – x|\) is attained at x = ?

A. 2
B. 4
C. 8
D. 10
E. 12


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions


Asked: The minimum value of \(f(x) = |10 – x| + |x – 2| – |4 – x|\) is attained at x = ?

At x=10
\(f(x) = |10 – x| + |x – 2| – |4 – x| = 0+8-6 = 2\) which is the minimum value of the function.

IMO D
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Intern
Intern
avatar
B
Joined: 14 Jan 2020
Posts: 34
GMAT 1: 760 Q51 V41
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 10 Jun 2020, 08:47
1
Bunuel wrote:
The minimum value of \(f(x) = |10 – x| + |x – 2| – |4 – x|\) is attained at x = ?

A. 2
B. 4
C. 8
D. 10
E. 12


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions


for this to be minimum -> \(f(x) = |10 – x| + |x – 2| – |4 – x|\) we need |10-x|+|x-2| to be minimum and |4-x| to be maximum
now, if we see the distance method approach:
|10-x|+|x-2| this is same as |x-10|+|x-2| ;
i.e. the sum of distance of x from ten and distance of x from 2, and, this remains at a constant value of 8 for all values of x from 2 to 10 & increase if x >10 or x<2
thus for |10-x|+|x-2| to be minimum we have to select an x value ranging from 2 to 10.
Now, |4-x| = |x-4| , i.e. this is the distance of x from 4,
So, for this value to be maximum we must select a value for x which is as farthest away from 4 as possible
given both these value conditions, we have x = 10 which is the farthest from 4 and gives minimum value for sum of distances from 2 and 10.
This would be the general approach,
Here however, substituting the values is a good and fast option, which may not be the case every time.
D
_________________
Reach out for personalized GMAT Coaching by a 99%iler
at-
prathyusha3@gmail.com
Intern
Intern
avatar
B
Joined: 19 Jan 2020
Posts: 2
Location: Spain
Concentration: Finance, Strategy
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 10 Mar 2020, 02:25
Shouldn't be 0+8+6 instead of 0+8-6?

Thank you
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 3339
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Reviews Badge CAT Tests
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 10 Mar 2020, 02:38
moneysniper365 wrote:
Shouldn't be 0+8+6 instead of 0+8-6?

Thank you


No since the function is of the form |x| + |y| - |z|
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6505
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 10 Mar 2020, 06:45
for given function value to get min value ; minimise the max possible in this case its 10
so \(f(x) = |10 – x| + |x – 2| – |4 – x|\) at x=10 gives minimum value
IMO D


Bunuel wrote:
The minimum value of \(f(x) = |10 – x| + |x – 2| – |4 – x|\) is attained at x = ?

A. 2
B. 4
C. 8
D. 10
E. 12


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions
Senior Manager
Senior Manager
User avatar
G
Joined: 05 Aug 2019
Posts: 330
Location: India
Concentration: Leadership, Technology
GMAT 1: 600 Q50 V22
GMAT 2: 670 Q50 V28 (Online)
GPA: 4
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 30 May 2020, 05:35
A - 2 => 8-2 = 6
B - 4 => 6+2 = 8
C - 8 => 2+6-4 = 4
D - 10 => 8-6 = 2
E - 12 => 2+10-8 = 4
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 5033
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 30 May 2020, 07:09
Bunuel wrote:
The minimum value of \(f(x) = |10 – x| + |x – 2| – |4 – x|\) is attained at x = ?

A. 2
B. 4
C. 8
D. 10
E. 12

Plug in the options and check

(A) 8 + 0 - 2 = 6
(B) 6 + 2 - 0 = 8
(C) 2 + 6 - 4 = 4
(D) 0 + 8 - 6 = 2
(E) 2 + 10 - 8 = 4

Thus, Answer must be (D)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
IESE School Moderator
avatar
G
Joined: 11 Feb 2019
Posts: 311
CAT Tests
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained  [#permalink]

Show Tags

New post 30 May 2020, 08:07
Is there any logic for similar questions?
|x| + |y| - |z|

I also solved using the substitution method.
_________________

Cheers,
NJ
GMAT Club Bot
Re: The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained   [#permalink] 30 May 2020, 08:07

The minimum value of f(x) = |10 – x| + |x – 2| – |4 – x| is attained

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





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