Author
Message
TAGS:

Hide Tags
Manager

Joined: 14 Dec 2011

Posts: 77

Kudos [? ]:
67 [2 ], given: 77

+1 Kudos

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

Show Tags
30 Oct 2012, 23:57
2

This post received KUDOS

30

This post was BOOKMARKED

Question Stats:

46% (01:34) correct

54% (01:31) wrong

based on 827 sessions

Hide Show 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

Official Answer and Stats are available only to registered users.

Register /

Login .

Last edited by

Bunuel on 31 Oct 2012, 03:04, edited 1 time in total.

Renamed the topic.

Kudos [? ]:
67 [2 ], given: 77

+1 Kudos

Director

Status: Done with formalities.. and back..

Joined: 15 Sep 2012

Posts: 634

Kudos [? ]:
693 [6 ], given: 23

+1 Kudos

Location: India

Concentration: Strategy, General Management

Schools: Olin - Wash U - Class of 2015

WE: Information Technology (Computer Software)

Re: function [#permalink ]

Show Tags
31 Oct 2012, 00:22
6

This post received KUDOS

4

This post was BOOKMARKED

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

Kudos [? ]:
693 [6 ], given: 23

+1 Kudos

Manager

Joined: 14 Dec 2011

Posts: 77

Kudos [? ]:
67 [1 ], given: 77

+1 Kudos

Re: function [#permalink ]

Show Tags
31 Oct 2012, 20:00
1

This post received KUDOS

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

Kudos [? ]:
67 [1 ], given: 77

+1 Kudos

Director

Status: Done with formalities.. and back..

Joined: 15 Sep 2012

Posts: 634

Kudos [? ]:
693 [1 ], given: 23

+1 Kudos

Location: India

Concentration: Strategy, General Management

Schools: Olin - Wash U - Class of 2015

WE: Information Technology (Computer Software)

Re: function [#permalink ]

Show Tags
31 Oct 2012, 20:31
1

This post received KUDOS

1

This post was BOOKMARKED

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

Kudos [? ]:
693 [1 ], given: 23

+1 Kudos

Senior Manager

Joined: 22 Nov 2010

Posts: 284

Kudos [? ]:
183 [2 ], given: 75

+1 Kudos

Location: India

WE: Consulting (Telecommunications)

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
20 Nov 2012, 09:23
2

This post received KUDOS

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

Kudos [? ]:
183 [2 ], given: 75

+1 Kudos

Manager

Joined: 23 Oct 2012

Posts: 55

Kudos [? ]:
66 [0 ], given: 285

+1 Kudos

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
21 Nov 2012, 20:32

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| ?

_________________

Kudos please!

Kudos [? ]:
66 [0 ], given: 285

+1 Kudos

Math Expert

Joined: 02 Sep 2009

Posts: 43312

Kudos [? ]:
139331 [4 ], given: 12783

+1 Kudos

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
22 Nov 2012, 04:23
Kudos [? ]:
139331 [4 ], given: 12783

+1 Kudos

Senior Manager

Joined: 22 Nov 2010

Posts: 284

Kudos [? ]:
183 [0 ], given: 75

+1 Kudos

Location: India

WE: Consulting (Telecommunications)

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
22 Nov 2012, 05:01

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

Kudos [? ]:
183 [0 ], given: 75

+1 Kudos

Math Expert

Joined: 02 Sep 2009

Posts: 43312

Kudos [? ]:
139331 [1 ], given: 12783

+1 Kudos

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
22 Nov 2012, 05:03
Kudos [? ]:
139331 [1 ], given: 12783

+1 Kudos

Manager

Joined: 23 Oct 2012

Posts: 55

Kudos [? ]:
66 [0 ], given: 285

+1 Kudos

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
05 Dec 2012, 20:58

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

_________________

Kudos please!

Kudos [? ]:
66 [0 ], given: 285

+1 Kudos

Intern

Joined: 29 Aug 2012

Posts: 1

Kudos [? ]:
[0 ], given: 3

+1 Kudos

Re: function [#permalink ]

Show Tags
09 Feb 2013, 03:08

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 ??

Kudos [? ]:
[0 ], given: 3

+1 Kudos

Math Expert

Joined: 02 Sep 2009

Posts: 43312

Kudos [? ]:
139331 [1 ], given: 12783

+1 Kudos

Re: function [#permalink ]

Show Tags
09 Feb 2013, 03:19
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.

_________________

New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders ; 8. Overlapping Sets | PDF of Math Book ; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years. Collection of Questions: PS: 1. Tough and Tricky questions ; 2. Hard questions ; 3. Hard questions part 2 ; 4. Standard deviation ; 5. Tough Problem Solving Questions With Solutions ; 6. Probability and Combinations Questions With Solutions ; 7 Tough and tricky exponents and roots questions ; 8 12 Easy Pieces (or not?) ; 9 Bakers' Dozen ; 10 Algebra set. ,11 Mixed Questions , 12 Fresh Meat DS: 1. DS tough questions ; 2. DS tough questions part 2 ; 3. DS tough questions part 3 ; 4. DS Standard deviation ; 5. Inequalities ; 6. 700+ GMAT Data Sufficiency Questions With Explanations ; 7 Tough and tricky exponents and roots questions ; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!! ; 10 Number Properties set. , 11 New DS set. What are GMAT Club Tests ? Extra-hard Quant Tests with Brilliant Analytics

Kudos [? ]:
139331 [1 ], given: 12783

+1 Kudos

Intern

Joined: 16 Dec 2012

Posts: 4

Kudos [? ]:
[0 ], given: 1

+1 Kudos

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
22 Feb 2013, 21:27

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.

Kudos [? ]:
[0 ], given: 1

+1 Kudos

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 7863

Kudos [? ]:
18465 [0 ], given: 237

+1 Kudos

Location: Pune, India

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
24 Feb 2013, 20:20
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 Veritas Prep | GMAT InstructorMy Blog Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews

Kudos [? ]:
18465 [0 ], given: 237

+1 Kudos

Manager

Joined: 28 Jul 2011

Posts: 233

Kudos [? ]:
168 [0 ], given: 16

+1 Kudos

Re: function [#permalink ]

Show Tags
16 Mar 2013, 20:16

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

Kudos [? ]:
168 [0 ], given: 16

+1 Kudos

Math Expert

Joined: 02 Sep 2009

Posts: 43312

Kudos [? ]:
139331 [0 ], given: 12783

+1 Kudos

Re: function [#permalink ]

Show Tags
17 Mar 2013, 00:57
Kudos [? ]:
139331 [0 ], given: 12783

+1 Kudos

Director

Joined: 29 Nov 2012

Posts: 861

Kudos [? ]:
1535 [0 ], given: 543

+1 Kudos

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
22 May 2013, 05:56

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

Kudos [? ]:
1535 [0 ], given: 543

+1 Kudos

VP

Status: Far, far away!

Joined: 02 Sep 2012

Posts: 1121

Kudos [? ]:
2437 [0 ], given: 219

+1 Kudos

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, 06:08

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]

Kudos [? ]:
2437 [0 ], given: 219

+1 Kudos

Director

Joined: 29 Nov 2012

Posts: 861

Kudos [? ]:
1535 [0 ], given: 543

+1 Kudos

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]

Show Tags
22 May 2013, 07:41

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

Kudos [? ]:
1535 [0 ], given: 543

+1 Kudos

VP

Status: Far, far away!

Joined: 02 Sep 2012

Posts: 1121

Kudos [? ]:
2437 [0 ], given: 219

+1 Kudos

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, 07:45

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]

Kudos [? ]:
2437 [0 ], given: 219

+1 Kudos

Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?
[#permalink ]
22 May 2013, 07:45

Go to page
1 2
Next
[ 25 posts ]