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

 It is currently 20 Jul 2018, 09:37

### 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

# What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Dec 2011
Posts: 75
What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

Updated on: 31 Oct 2012, 04:04
2
33
00:00

Difficulty:

95% (hard)

Question Stats:

47% (01:36) correct 53% (01:30) wrong based on 902 sessions

### HideShow timer Statistics

Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

What is wrong with

Thanks & Regards
Vinni

Originally posted by vinnik on 31 Oct 2012, 00:57.
Last edited by Bunuel on 31 Oct 2012, 04:04, edited 1 time in total.
Renamed the topic.
Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 616
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)

### Show Tags

31 Oct 2012, 01:22
6
4
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..
_________________

Lets Kudos!!!
Black Friday Debrief

##### General Discussion
Manager
Joined: 14 Dec 2011
Posts: 75

### Show Tags

31 Oct 2012, 21:00
1
Vips0000 wrote:
From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Well, I haven't understood completely.
All i know from my knowledge that |a - b| = |b - a|
So, as you have explained above |x-5|- |x-5| = 0
Now we are left with |-x|
According to what i have read from the books, any absolute value whether negative or positive will come out as positive. For eg. |-5| = 5.
This is the exact reason i selected E as the answer.

I must be missing one of the concepts. Can you please elaborate more on it. I didn't completely understand this statement "It can not be E because x <> |x| for any negative value of x."

Thanks & Regards
Vinni
Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 616
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)

### Show Tags

31 Oct 2012, 21:31
1
1
vinnik wrote:
Vips0000 wrote:
From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Well, I haven't understood completely.
All i know from my knowledge that |a - b| = |b - a|
So, as you have explained above |x-5|- |x-5| = 0
Now we are left with |-x|
According to what i have read from the books, any absolute value whether negative or positive will come out as positive. For eg. |-5| = 5.
This is the exact reason i selected E as the answer.

I must be missing one of the concepts. Can you please elaborate more on it. I didn't completely understand this statement "It can not be E because x <> |x| for any negative value of x."

Thanks & Regards
Vinni

Two points that you are confused with:
|-x| = |x|
This is exactly same thing as you have mentioned:
"All i know from my knowledge that |a - b| = |b - a|"

Now second point,
x <> |x| for any negative number x.

Well, take for example x =-5
in this case, x= -5 and |x|=5
Are these 5 and -5 equal? no.
That is x <> |x| for any negative number x.

What you are confusing this is with |x|=|-x|

Hope it is clear.
_________________

Lets Kudos!!!
Black Friday Debrief

Senior Manager
Joined: 22 Nov 2010
Posts: 256
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

20 Nov 2012, 10:23
2
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

What is wrong with

Thanks & Regards
Vinni

how i solved this ques:

|f(x)| - |g(x)| = 0. Because, f(x) and g(x) both represents distance between x & 5.

Therefore, we have to solve only this |f(g(x)| => |f(5-x)|= |5-x-5| = |x|
_________________

YOU CAN, IF YOU THINK YOU CAN

Manager
Joined: 23 Oct 2012
Posts: 51
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

21 Nov 2012, 21:32
greatps24 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

What is wrong with

Thanks & Regards
Vinni

how i solved this ques:

|f(x)| - |g(x)| = 0. Because, f(x) and g(x) both represents distance between x & 5.

Therefore, we have to solve only this |f(g(x)| => |f(5-x)|= |5-x-5| = |x|

I am confused as in the value of |-x| will always be x so why are we choosing |x| ?
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 47152
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

22 Nov 2012, 05:23
4
2013gmat wrote:
greatps24 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

What is wrong with

Thanks & Regards
Vinni

how i solved this ques:

|f(x)| - |g(x)| = 0. Because, f(x) and g(x) both represents distance between x & 5.

Therefore, we have to solve only this |f(g(x)| => |f(5-x)|= |5-x-5| = |x|

I am confused as in the value of |-x| will always be x so why are we choosing |x| ?

|-x|=|x| for all x's. Now, if x<0, then |-x|=|x|=-x but if x>=0, then |-x|=|x|=x.

Hope it's clear.
_________________
Senior Manager
Joined: 22 Nov 2010
Posts: 256
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

22 Nov 2012, 06:01
Kudos Bunuel. Thanks for clarifying

One point: what if in answer choices we also have |-x| (and |x|)?
_________________

YOU CAN, IF YOU THINK YOU CAN

Math Expert
Joined: 02 Sep 2009
Posts: 47152
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

22 Nov 2012, 06:03
1
greatps24 wrote:
Kudos Bunuel. Thanks for clarifying

One point: what if in answer choices we also have |-x| (and |x|)?

|-x| and |x| are equal, thus we cannot have both of them among answer choices. Consider this, can we have both 4 and 2^2 among answer choices?
_________________
Manager
Joined: 23 Oct 2012
Posts: 51
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

05 Dec 2012, 21:58
Bunuel wrote:
greatps24 wrote:
Kudos Bunuel. Thanks for clarifying

One point: what if in answer choices we also have |-x| (and |x|)?

|-x| and |x| are equal, thus we cannot have both of them among answer choices. Consider this, can we have both 4 and 2^2 among answer choices?

Kudos Bunuel. Cheers
_________________

Intern
Joined: 29 Aug 2012
Posts: 1

### Show Tags

09 Feb 2013, 04:08
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Got a doubt...

f(g(x)| = |f(5-x)| = |5-x-5| =|-x|
Why (5-x) is considered without Mod sign. Ideally it should have been |f(|5-x|)| = |(|5-x|)-5|
If we simplify this we get two options |x-10| and |x|.
Why this is not correct ??
Math Expert
Joined: 02 Sep 2009
Posts: 47152

### Show Tags

09 Feb 2013, 04:19
1
mani6389 wrote:
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Got a doubt...

f(g(x)| = |f(5-x)| = |5-x-5| =|-x|
Why (5-x) is considered without Mod sign. Ideally it should have been |f(|5-x|)| = |(|5-x|)-5|
If we simplify this we get two options |x-10| and |x|.
Why this is not correct ??

|f(g(x))| has only one modulus.

g(x)=5-x, thus |f(g(x))| = |f(5-x)|.

Next, since f(5-x) = 5-x-5=-x, then |f(5-x)| = |-x| = |x|.

Hope it's clear.
_________________
Intern
Joined: 16 Dec 2012
Posts: 4
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

22 Feb 2013, 22:27
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

hi in the above question it is asking the value of the equation
|f(x)| - |g(x)| + |f(g(x)|....

when we put in the values appropriately:

|x-5|-|5-x|+|5-x-5|
=|-x|

mod of -x=x

i understand the piece tht

when we have the value as -x and we take modulous then it gives the values
as positive values of x.

|-x| is not equal to x

but here it is asking us the eventual result of the equation
so when we get |-x| we get the final result, it is positive values of x.
GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8132
Location: Pune, India
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

24 Feb 2013, 21:20
mehasingh wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

hi in the above question it is asking the value of the equation
|f(x)| - |g(x)| + |f(g(x)|....

when we put in the values appropriately:

|x-5|-|5-x|+|5-x-5|
=|-x|

mod of -x=x

i understand the piece tht

when we have the value as -x and we take modulous then it gives the values
as positive values of x.

|-x| is not equal to x

but here it is asking us the eventual result of the equation
so when we get |-x| we get the final result, it is positive values of x.

You are assuming that x is positive.

|-x| = |x| in any case. x may be positive or negative. Take examples:
Say x = 5, |-5| = |5| = 5
Say x = -5, |-(-5)| = |-5| = 5
Hence (C) is correct.

But to remove the mod, you must know the sign of x.

By definition,
|x| = x when x is positive
|x| = -x when x is negative

|-x| = |x| = x only when x is positive
If x is negative, say x = -1,
|-x| = |-(-1)| = 1 which is not the same as x.

Hence $$|-x| \neq x$$ when x is negative.
Since we have no information on the sign of x, we cannot say that |-x| = x.
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Manager
Joined: 28 Jul 2011
Posts: 208

### Show Tags

16 Mar 2013, 21:16
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Can any1 explain why

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

|5-x| = |x-5| ???

Thank you
Math Expert
Joined: 02 Sep 2009
Posts: 47152

### Show Tags

17 Mar 2013, 01:57
kuttingchai wrote:
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Can any1 explain why

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

|5-x| = |x-5| ???

Thank you

Yes, |5-x| = |x-5|, because both represent the distance between x and 5.
_________________
Director
Joined: 29 Nov 2012
Posts: 818
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

22 May 2013, 06:56
one more question if we were given X is positive or negative then the answer would be E?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1098
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

22 May 2013, 07:08
fozzzy wrote:
one more question if we were given X is positive or negative then the answer would be E?

Not sure of what you mean, but the answer is C for every value of x (+ve, -ve or =0)
_________________

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

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Director
Joined: 29 Nov 2012
Posts: 818
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

22 May 2013, 08:41
As per Vips000 solution after you solve we get $$=|x|$$

now if we were given an additional constraint that X is positive then we can solve for the modulus right?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1098
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

### Show Tags

22 May 2013, 08:45
fozzzy wrote:
As per Vips000 solution after you solve we get $$=|x|$$

now if we were given an additional constraint that X is positive then we can solve for the modulus right?

If we know that x is positive then we can solve the modulus and obtain $$|x|=x$$, yes you're right.

But be careful, in this case both c and e would be correct

C). $$|x|$$ => $$x$$

E). $$x$$
They are the same.

Hope it's clear
_________________

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

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? &nbs [#permalink] 22 May 2013, 08:45

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.