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

It is currently 21 Jan 2019, 17:00

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

     January 21, 2019

     January 21, 2019

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
  • The winners of the GMAT game show

     January 22, 2019

     January 22, 2019

     10:00 PM PST

     11:00 PM PST

    In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.

M19-14

  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: 52344
M19-14  [#permalink]

Show Tags

New post 16 Sep 2014, 00:06
1
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (00:46) correct 46% (00:57) wrong based on 213 sessions

HideShow timer Statistics

If \(f(x) = \frac{x}{x + 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(1 - f(x)\)
E. none of the above

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52344
Re M19-14  [#permalink]

Show Tags

New post 16 Sep 2014, 00:06
1
1
Official Solution:

If \(f(x) = \frac{x}{x + 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(1 - f(x)\)
E. none of the above

\(f(\frac{1}{x})= \frac{\frac{1}{x}}{\frac{1}{x} + 1} = \frac{1}{1 + x} = \frac{1 + x - x}{1 + x} = 1 - \frac{x}{1 + x} = 1 - f(x)\).

Answer: D
_________________

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

Manager
Manager
avatar
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)
Premium Member
Re: M19-14  [#permalink]

Show Tags

New post 27 Oct 2014, 18:21
1
Hi,

How did you get from 1/(1+x) to (1+x-x)/(1+x), and then from this to the final step?

Thanks
Intern
Intern
avatar
Joined: 30 Jul 2014
Posts: 4
GMAT 1: 540 Q40 V25
GMAT 2: 580 Q47 V24
Re: M19-14  [#permalink]

Show Tags

New post 28 Oct 2014, 04:05
6
JackSparr0w

To solve this question,

First find the value of f(1/x). To do this, replace x with 1/x in the equation.

so f(1/x)=(1/x)/((1/x)+1) = 1/1+x

Now check which option will give you 1/1+x.

Option A : f(x) = x/x+1 not equal..

Option B : -f(x) = -x/x+1 not equal..

Option C : 1/f(x) = x+1/x not equal..

Option D : 1-f(x) = 1-(x/x+1) =(x+1-x)/x+1 = 1/x+1 .. This is the answer.

Option E : None..


+1 Kudos if this helps..
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52344
Re: M19-14  [#permalink]

Show Tags

New post 28 Oct 2014, 04:09
2
1
JackSparr0w wrote:
Hi,

How did you get from 1/(1+x) to (1+x-x)/(1+x), and then from this to the final step?

Thanks


\(f(\frac{1}{x})= \frac{\frac{1}{x}}{\frac{1}{x} + 1} =\).

\(\frac{\frac{1}{x}}{(\frac{1+x}{x})} =\)

\(\frac{1}{x}*\frac{x}{x+1}\)

\(=\frac{1}{1 + x} =\)

\(=\frac{(1 + x) - x}{1 + x} =\)

\(=\frac{(1 + x)}{1 + x}-\frac{x}{1+x}=\)

\(=1 - \frac{x}{1 + x} =\)

\(=1 - f(x)\)
_________________

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

Manager
Manager
avatar
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)
Premium Member
Re: M19-14  [#permalink]

Show Tags

New post 03 Nov 2014, 20:06
2
msaid007 wrote:
JackSparr0w

To solve this question,

First find the value of f(1/x). To do this, replace x with 1/x in the equation.

so f(1/x)=(1/x)/((1/x)+1) = 1/1+x

Now check which option will give you 1/1+x.

Option A : f(x) = x/x+1 not equal..

Option B : -f(x) = -x/x+1 not equal..

Option C : 1/f(x) = x+1/x not equal..

Option D : 1-f(x) = 1-(x/x+1) =(x+1-x)/x+1 = 1/x+1 .. This is the answer.

Option E : None..


+1 Kudos if this helps..


Thanks! Got it!

For others, I think it may be helpful to elaborate on one other point. After you find that f(1/x) = 1/(1+x), compare this to the answer choices by substituting a value for x.

Ex: (assume x = 2). When x is 2, 1/(1+x) becomes 1/(1+2) or (1/3).

We also know f(x) = x/(x+1) from the question stem. So when x=2, f(x)=2/(2+1), or 2/3. We need to find the answer choice that changes 2/3 to 1/3.

Knowing this we can see that choice D is correct. Choice D is 1-f(x), or 1-(2/3) which equals 1/3; the same as our answer above.
Manager
Manager
avatar
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)
Premium Member
Re: M19-14  [#permalink]

Show Tags

New post 03 Nov 2014, 20:08
1
Bunuel wrote:
JackSparr0w wrote:
Hi,

How did you get from 1/(1+x) to (1+x-x)/(1+x), and then from this to the final step?

Thanks


\(f(\frac{1}{x})= \frac{\frac{1}{x}}{\frac{1}{x} + 1} =\).

\(\frac{\frac{1}{x}}{(\frac{1+x}{x})} =\)

\(\frac{1}{x}*\frac{x}{x+1}\)

\(=\frac{1}{1 + x} =\)

\(=\frac{(1 + x) - x}{1 + x} =\)

\(=\frac{(1 + x)}{1 + x}-\frac{x}{1+x}=\)

\(=1 - \frac{x}{1 + x} =\)

\(=1 - f(x)\)


Thanks Bunuel, much appreciated!. I think I'll have to use the substitution approach here, though.
Manager
Manager
avatar
Joined: 24 Nov 2013
Posts: 57
Re: M19-14  [#permalink]

Show Tags

New post 12 Oct 2015, 17:38
1
Bunuel

I was able to get f(1/x)= 1/1+x.
this is nothing but (x)/(x)(1+x)

and we know f(x) = x/x+1
therefore f(1/x) = f(x) divided by x
but this is not available in the options. Hence I chose E.

Could you please tell me what is wrong with this approach. Thanks.
Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
Premium Member
Re: M19-14  [#permalink]

Show Tags

New post 15 Aug 2016, 06:50
1
Bunuel wrote:
If \(f(x) = \frac{x}{x + 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(1 - f(x)\)
E. none of the above
[quote="Bunuel"]If \(f(x) = \frac{x}{x + 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

f(x) =x/(x+1) let's x = 2, then f(x) = 2/(2+1) = 2/3 and f(1/x) = (1/2)/(3/2) = 1/3

Now f(x) = 2/3, plug in 2/3 into the answer choices starting with choice D. Even before you start plugging in, you realise that D is the only answer choice that will result in 1/3 = f(1/x)
_________________

Kindly press kudos if you find my post helpful

Intern
Intern
avatar
Joined: 18 May 2016
Posts: 6
Re: M19-14  [#permalink]

Show Tags

New post 15 Dec 2016, 00:06
1
Bunuel wrote:
JackSparr0w wrote:
Hi,

How did you get from 1/(1+x) to (1+x-x)/(1+x), and then from this to the final step?

Thanks


\(f(\frac{1}{x})= \frac{\frac{1}{x}}{\frac{1}{x} + 1} =\).

\(\frac{\frac{1}{x}}{(\frac{1+x}{x})} =\)

\(\frac{1}{x}*\frac{x}{x+1}\)

\(=\frac{1}{1 + x} =\)

\(=\frac{(1 + x) - x}{1 + x} =\)

\(=\frac{(1 + x)}{1 + x}-\frac{x}{1+x}=\)

\(=1 - \frac{x}{1 + x} =\)

\(=1 - f(x)\)


Can you explain the reasoning behind the highlighted steps please
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52344
Re: M19-14  [#permalink]

Show Tags

New post 15 Dec 2016, 02:37
1
1
bjklue wrote:
Bunuel wrote:
JackSparr0w wrote:
Hi,

How did you get from 1/(1+x) to (1+x-x)/(1+x), and then from this to the final step?

Thanks


\(f(\frac{1}{x})= \frac{\frac{1}{x}}{\frac{1}{x} + 1} =\).

\(\frac{\frac{1}{x}}{(\frac{1+x}{x})} =\)

\(\frac{1}{x}*\frac{x}{x+1}\)

\(=\frac{1}{1 + x} =\)

\(=\frac{(1 + x) - x}{1 + x} =\)

\(=\frac{(1 + x)}{1 + x}-\frac{x}{1+x}=\)

\(=1 - \frac{x}{1 + x} =\)

\(=1 - f(x)\)


Can you explain the reasoning behind the highlighted steps please



By isolating x/(1+x) we are able to get f(x) in the expression.
_________________

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

Intern
Intern
avatar
B
Joined: 29 Aug 2016
Posts: 21
GMAT 1: 490 Q36 V22
GPA: 3
Reviews Badge
Re: M19-14  [#permalink]

Show Tags

New post 16 Jan 2017, 21:43
1
I have reached the substitution but unable to get the process after that...
Intern
Intern
avatar
B
Joined: 02 Jun 2015
Posts: 23
Location: United States
Re: M19-14  [#permalink]

Show Tags

New post 30 May 2018, 14:51
Tanyanagra wrote:
I have reached the substitution but unable to get the process after that...


Hi Tanyanagra,

For me using substitution is better than trying to manipulate the variables, especially under pressure....here's how I solve it !

Substitute x=2 into this 1st equation: f(x) = x divided by x+1 f(2) = 2 divided by 2+1 = 2/3

Then, the question asks what is f(1/x) in terms of f(x)?

You'll need to convert the f(x) to f(1/x) that will be 1/x divided by 1/x+1

Substitute x=2 into this 2nd equation f(1/x): 1/2 divided by 1/2+1 = 1/2 divided by 3/2 = 1/2 * 2/3 = 1/3

Now, you have to find 1/3in the answer choices:

A) f(x) = 2/3 not a match

B) - f(x) = - 2/3 not a match

C) 1/f(x) = 1 divided by 2/3 = 3/2 not a match

D) 1 - f(x) = 1 - 2/3 = 1/3 BINGO!! That's a match

E) none of the above = wrong

I hope it helps!

Thanks Ale! :-)
Manager
Manager
avatar
B
Joined: 26 Sep 2018
Posts: 57
Location: Sweden
CAT Tests
Re: M19-14  [#permalink]

Show Tags

New post 30 Dec 2018, 11:53
In problems like these, one of the best ways to solve is by plugging in numbers.

For example:

x=5 and 1/x = 1/5.

So f(5)=5/6 and f(1/5)= 1/6, only option d works.

Try x= 1/3 to confirm. Admittedly not the best method, but it does the trick!
GMAT Club Bot
Re: M19-14 &nbs [#permalink] 30 Dec 2018, 11:53
Display posts from previous: Sort by

M19-14

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

Moderators: chetan2u, Bunuel



Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.