Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 10 Mar 2014, 20:21

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If f(x)= |4x - 1| + |x-3| + |x + 1| (Question of the Day-II)

Author Message
TAGS:
Manager
Joined: 25 Aug 2011
Posts: 197
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
Followers: 1

Kudos [?]: 39 [0], given: 11

Re: Question of the Day - II [#permalink]  20 Mar 2012, 21:20
Karishma,
Is there a way to solve this by setting boiundary conditions. ie. x<-1,-1<x<1/4,1/4<x<3,x>3??
I tried but wasnt able to make sense

VeritasPrepKarishma wrote:
Q. If f(x) = |4x - 1| + |x-3| + |x + 1|, what is the minimum value of f(x)?

(A) 3
(B) 4
(C) 5
(D) 21/4
(E) 7

(Still high on mods! Next week, will make questions on some other topic.)
 Veritas Prep GMAT Discount Codes Knewton GMAT Discount Codes Kaplan GMAT Prep Discount Codes
Intern
Joined: 26 May 2012
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Question of the Day - II [#permalink]  26 May 2012, 11:00
VeritasPrepKarishma wrote:
Q. If f(x) = |4x - 1| + |x-3| + |x + 1|, what is the minimum value of f(x)?

(A) 3
(B) 4
(C) 5
(D) 21/4
(E) 7

(Still high on mods! Next week, will make questions on some other topic.)

for any value of X , term |4x-1| must give maximum value, so anything that gives lowest of |4x-1| will give lowest for f(x), so x=1/4 and F(x) is 4, B
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4032
Location: Pune, India
Followers: 860

Kudos [?]: 3618 [0], given: 144

Re: Question of the Day - II [#permalink]  04 Jun 2012, 18:48
Expert's post
devinawilliam83 wrote:
Karishma,
Is there a way to solve this by setting boiundary conditions. ie. x<-1,-1<x<1/4,1/4<x<3,x>3??
I tried but wasnt able to make sense

VeritasPrepKarishma wrote:
Q. If f(x) = |4x - 1| + |x-3| + |x + 1|, what is the minimum value of f(x)?

(A) 3
(B) 4
(C) 5
(D) 21/4
(E) 7

(Still high on mods! Next week, will make questions on some other topic.)

If you mean whether you can make equations using positive and negative values, you cant do that with minimum/maximum questions. You don't really have a value to equate them to.
e.g. |4x - 1| + |x-3| + |x + 1| = 10 is workable but minimum value of f(x) isn't. You will need to find the value at the critical points and then figure how f(x) changes or just use the number line.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4032 Location: Pune, India Followers: 860 Kudos [?]: 3618 [0], given: 144 Re: Question of the Day - II [#permalink] 04 Jun 2012, 19:06 Expert's post koro12 wrote: VeritasPrepKarishma wrote: Q. If f(x) = |4x - 1| + |x-3| + |x + 1|, what is the minimum value of f(x)? (A) 3 (B) 4 (C) 5 (D) 21/4 (E) 7 (Still high on mods! Next week, will make questions on some other topic.) for any value of X , term |4x-1| must give maximum value, so anything that gives lowest of |4x-1| will give lowest for f(x), so x=1/4 and F(x) is 4, B Beware of using this logic in other similar questions e.g. f(x) = |2x - 1| + |x-3| + |x - 1| + |x - 5| or f(x) = |3x + 1| + |2x-3| + |2x - 7| _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Joined: 01 Apr 2012
Posts: 26
Location: United States
Concentration: Technology, Economics
GMAT Date: 05-13-2012
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 10 [0], given: 18

Re: Question of the Day - II [#permalink]  04 Jun 2012, 22:09
Hi Karishma...

Can you please explain the example which has negative between the modulus (could not understand fully the explaination given by you earlier). Also if in a question we have a combination of + and - then how to go about it?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4032
Location: Pune, India
Followers: 860

Kudos [?]: 3618 [1] , given: 144

Re: Question of the Day - II [#permalink]  05 Jun 2012, 05:22
1
KUDOS
Expert's post
ankitbansal85 wrote:
Hi Karishma...

Can you please explain the example which has negative between the modulus (could not understand fully the explaination given by you earlier). Also if in a question we have a combination of + and - then how to go about it?

When you add two mods, you try to add up the distances e.g.
|x - 1| + |x - 5| = 10
you try to find the point where distance from 1 and distance from 5 adds up to give you 10.

When you subtract two mods, you subtract out the distances e.g.
|x - 1| - |x - 5| = 3
you try to find the point where distance from 1 and distance from 5 have a difference of 3. You know that at x = 3, distances from 1 and from 5 are equal (distance of 1 from 3 is 2 and distance of 5 from 3 is also 2). At x = 4, the difference between the distances will be 2. At x = 4.5, the difference between the distances will be 3.

The subtraction is a little less intuitive and will take more practice. Questions with both + and - would be too complicated though do-able. Most people will probably not get any mods question with more than 2 terms.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Senior Manager Joined: 13 Aug 2012 Posts: 465 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 14 Kudos [?]: 148 [0], given: 11 Re: Question of the Day - II [#permalink] 06 Dec 2012, 04:06 I love this question. One must understand that f(x) = |4x-1| + |x-3| + |x+1| means the sum of the distances of x to 1/4, 3 and -1. The best way to minimize is to zero out the distance in the middle. ==========(-1)==========(0)======(1/4)=========(3)======= So if x = 1/4 |4x-1| = 0 |x+1| = 1 1/4 |x-3| = 2 3/4 Answer: 4 _________________ Impossible is nothing to God. Manager Joined: 24 Mar 2010 Posts: 82 Followers: 0 Kudos [?]: 14 [0], given: 134 Re: Question of the Day - II [#permalink] 16 Dec 2012, 20:57 Karishma, So from your method, I infer That minimum of a function will always be at either its critical points or zero. Await your valued response. _________________ - Stay Hungry, stay Foolish - Manager Joined: 24 Mar 2010 Posts: 82 Followers: 0 Kudos [?]: 14 [0], given: 134 Re: Question of the Day - II [#permalink] 16 Dec 2012, 21:06 Karishma, For my better understanding of the subject, lets find the minimum of the function below. f(x) = |x - 1| - |x - 5| x = 0 :: f(x) = -4 x = 1 :: f(x) = -4 x = 5 :: f(x) = 4 Is this correct? _________________ - Stay Hungry, stay Foolish - Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4032 Location: Pune, India Followers: 860 Kudos [?]: 3618 [0], given: 144 Re: Question of the Day - II [#permalink] 17 Dec 2012, 03:30 Expert's post eaakbari wrote: Karishma, So from your method, I infer That minimum of a function will always be at either its critical points or zero. Await your valued response. The minimum could also be in an entire range. Take this question for example. f(x) = |3x + 1| + |2x-3| + |x - 7| For what value(s) of x will f(x) have the minimum value? _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Joined: 24 Mar 2010
Posts: 82
Followers: 0

Kudos [?]: 14 [0], given: 134

Re: Question of the Day - II [#permalink]  17 Dec 2012, 07:25
VeritasPrepKarishma wrote:
eaakbari wrote:
Karishma,

So from your method, I infer

That minimum of a function will always be at either its critical points or zero.

The minimum could also be in an entire range. Take this question for example.

f(x) = |3x + 1| + |2x-3| + |x - 7|

For what value(s) of x will f(x) have the minimum value?

----------- -1/3 ------------------ 0 ----------------------- 3/2 ---------------------------------------------7 -------------------------

Method that I prev used to solve.

x = -1/3 => f(x) = -11
x = 3/2 => f(x) = 0
x = 7 => f(x) = 33

So x = 3/2 is point of where f(x) = 0

Am I right.

Since 3/2 is the middle value in between -1/3 & 7. The distance will be the least at 3/2...

Have I inferred correctly?
_________________

- Stay Hungry, stay Foolish -

Manager
Joined: 24 Mar 2010
Posts: 82
Followers: 0

Kudos [?]: 14 [0], given: 134

Re: Question of the Day - II [#permalink]  17 Dec 2012, 07:29
Karishma,

What about a function with evenly spaced numbers?

for instance

f(x) = | 4x + 1| + | 2x + 1| + | 4x + 3| + | x |

What will be the min. value of x for this?
_________________

- Stay Hungry, stay Foolish -

SVP
Joined: 05 Jul 2006
Posts: 1543
Followers: 4

Kudos [?]: 51 [0], given: 39

Re: Question of the Day - II [#permalink]  12 May 2013, 11:09
What if the question asks for max value of f(x) ??? disregarding the answer choices ??
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4032
Location: Pune, India
Followers: 860

Kudos [?]: 3618 [0], given: 144

Re: Question of the Day - II [#permalink]  13 May 2013, 08:52
Expert's post
yezz wrote:
What if the question asks for max value of f(x) ??? disregarding the answer choices ??

Not every function will have a minimum and a maximum value. The greater the value of x, the greater the function will become. It is an infinitely increasing function.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Intern Joined: 24 Mar 2013 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Question of the Day - II [#permalink] 19 May 2013, 16:08 Many Thanks to all of you for sharing such amazing techniques. I was overwhelmed with mod questions when I started, but your explanations and techniques have helped me build confidence. Bunuel, Karishma, Gurpreet, Shrouded1....Awesome! How about this approach: F(x) will be minimum when each individual term in the function has the lowest possible value. So, I get x = 3, -1 and 1/4. Now, substituting each value of x in F(x), I can easily see that x=1/4 gives me the smallest possible value for F(x) = 4 Thanks, Rohit Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4032 Location: Pune, India Followers: 860 Kudos [?]: 3618 [0], given: 144 Re: Question of the Day - II [#permalink] 20 May 2013, 06:07 Expert's post eaakbari wrote: Karishma, What about a function with evenly spaced numbers? for instance f(x) = | 4x + 1| + | 2x + 1| + | 4x + 3| + | x | What will be the min. value of x for this? The function will take a minimum value for a range of values of x (between the second and the third values). Think 'Why?' _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4032
Location: Pune, India
Followers: 860

Kudos [?]: 3618 [1] , given: 144

Re: Question of the Day - II [#permalink]  20 May 2013, 06:14
1
KUDOS
Expert's post
rohitd80 wrote:
Many Thanks to all of you for sharing such amazing techniques. I was overwhelmed with mod questions when I started, but your explanations and techniques have helped me build confidence. Bunuel, Karishma, Gurpreet, Shrouded1....Awesome!

F(x) will be minimum when each individual term in the function has the lowest possible value. So, I get x = 3, -1 and 1/4.
Now, substituting each value of x in F(x), I can easily see that x=1/4 gives me the smallest possible value for F(x) = 4

Thanks,
Rohit

The technique is fine but the logic is not sound. Why should we say that the function will take minimum value only when it takes one of these three values? For one of these values, sure one mod will be 0 but the other two could be much greater.
The reason why this works is because the minimum value will be at one of the transition points - the middle point (logic explained in the post on previous page) in case there are odd number of terms OR at two points (and for every value in between) in case there are even number of terms.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save \$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Joined: 13 May 2013
Posts: 476
Followers: 0

Kudos [?]: 35 [0], given: 134

Re: Question of the Day - II [#permalink]  28 May 2013, 13:04
Hello all.

I am wondering why we cannot take the positive and negative cases of f(x) = |4x - 1| + |x-3| + |x + 1| and solve for x that way?

In other words, f(x) = |4x - 1| + |x-3| + |x + 1|

I. f(x) = (4x-1) + (x-3) + (x+1)

II. f(x) = -(4x-1) + -(x-3) + -(x-1)

Thanks!
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 88

Kudos [?]: 985 [1] , given: 219

Re: Question of the Day - II [#permalink]  28 May 2013, 13:56
1
KUDOS
WholeLottaLove wrote:
Hello all.

I am wondering why we cannot take the positive and negative cases of f(x) = |4x - 1| + |x-3| + |x + 1| and solve for x that way?

In other words, f(x) = |4x - 1| + |x-3| + |x + 1|

I. f(x) = (4x-1) + (x-3) + (x+1)

II. f(x) = -(4x-1) + -(x-3) + -(x-1)

Thanks!

It's not that easy!

if you wanna study the absolute value, more math is required.
You have to study each abs>0 so
4x-1>0 and x-3>0 and x+1>0
x>\frac{1}{4} and x>3 and x>-1
so 4x-1 is positive for x>1/4, x-3 is +ve for x>3 and x-1 is +ve for x>-1

Now you have to split the original function into the areas defined above:
x<-1 all functions are negative
f(x) = -(4x-1) + -(x-3) + -(x-1)
if -1<x<\frac{1}{4} the third term is positive,the others negative
f(x) = -(4x-1) + -(x-3) +(x-1)
and so on...

You cannot take all positive or all negative, you have to study each function in all possible intervals
Below there is the graph of F(x) that I hope will make thing clear. As you see there are 4 functions, each one defined in the intervals above, so your way of studying the abs value (reducing all to 2 functions) is incomplete

Hope it's clear
Attachments

Untitled.png [ 5.15 KiB | Viewed 605 times ]

_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Senior Manager
Joined: 13 May 2013
Posts: 476
Followers: 0

Kudos [?]: 35 [0], given: 134

Re: Question of the Day - II [#permalink]  28 May 2013, 14:06
Ok, I get that for f(x) = (4x-1) + (x-3) + (x+1), x must be greater than 1/4, 3 and -1 respectively. But that's where I get lost.

I'm sorry for being so dense on this topic!
Re: Question of the Day - II   [#permalink] 28 May 2013, 14:06
Similar topics Replies Last post
Similar
Topics:
Is x > 0? (1) |x + 3| = 4x 3 (2) |x 3| = |2x 3 8 01 Jul 2007, 08:52
Is x > 0, 1. |x + 3| = 4x - 3 2. |x - 3| = |2x -3| 6 18 Aug 2007, 15:13
Is x > 0? (1) |x + 3| = 4x 3 (2) |x 3| = |2x 3 8 31 Oct 2007, 06:49
Is x > 0? (1) |x + 3| = 4x 3 (2) |x 3| = |2x 3 11 24 Nov 2007, 05:37
Is x > 0? (1) |x + 3| = 4x 3 (2) |x 3| = |2x 3 7 30 Mar 2008, 11:46
Display posts from previous: Sort by