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

It is currently 22 Sep 2018, 19:44

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

M20-26

  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: 49303
M20-26  [#permalink]

Show Tags

New post 16 Sep 2014, 01:09
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (00:47) correct 26% (01:25) wrong based on 134 sessions

HideShow timer Statistics

If \(f(x) = \frac{x^4 - 1}{x^2}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(-\frac{1}{f(x)}\)
E. \(2f(x)\)

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re M20-26  [#permalink]

Show Tags

New post 16 Sep 2014, 01:09
Official Solution:

If \(f(x) = \frac{x^4 - 1}{x^2}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(-\frac{1}{f(x)}\)
E. \(2f(x)\)

\(f(\frac{1}{x}) = \frac{\frac{1}{x^4} - 1}{\frac{1}{x^2}} = \frac{1}{x^2} - x^2 = \frac{1 - x^4}{x^2} = -f(x)\).

Answer: B
_________________

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
Joined: 05 Jul 2016
Posts: 5
Re: M20-26  [#permalink]

Show Tags

New post 14 Jul 2016, 11:27
Hello,

Can you please explain how the last step works. ie how does (1-x^4)/x^2= -f(x)

Thanks!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: M20-26  [#permalink]

Show Tags

New post 15 Jul 2016, 07:35
2
Intern
Intern
avatar
B
Joined: 29 Jul 2017
Posts: 3
Re: M20-26  [#permalink]

Show Tags

New post 11 Sep 2017, 04:23
Can you explain how you get 1/x^2 - x^2?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: M20-26  [#permalink]

Show Tags

New post 11 Sep 2017, 04:46
1
Director
Director
User avatar
S
Joined: 08 Jun 2015
Posts: 503
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33
Premium Member CAT Tests
Re: M20-26  [#permalink]

Show Tags

New post 18 Oct 2017, 05:54
Substitute (1/x) in f(x). You will get -f(x). The answer is option B.
_________________

" The few , the fearless "

Manager
Manager
User avatar
B
Joined: 03 May 2017
Posts: 106
GMAT ToolKit User
M20-26  [#permalink]

Show Tags

New post 18 Oct 2017, 23:06
2
\(\)
Bunuel wrote:
If \(f(x) = \frac{x^4 - 1}{x^2}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(-\frac{1}{f(x)}\)
E. \(2f(x)\)



Just plug in \(\frac{1}{2}\) and \(2\), then compare the answers.

For \(f(\frac{1}{2})\), you had get \((\frac{1}{16} -1) / \frac{1}{4} = \frac{-15}{4}\)

and for \(f(2)\), you had get \(\frac{15}{4}\) i.e \(\frac{(16-1)}{4}\)

Thus \(f(\frac{1}{x})\) = \(-f(x)\), which is B.

alternatively, algebraically, \(f(x) = \frac{x^4 - 1}{x^2}\) = \(x^2 - \frac{1}{x^2}\)

One can quickly see the pattern and know that the function is negatively symmetrical for the reciprocal i.e let \(x^2 =\frac{1}{2}\), then \(x^2 - \frac{1}{x^2}\)= negative and positive same value if \(x^2 =2\). Again, B.
GMAT Club Bot
M20-26 &nbs [#permalink] 18 Oct 2017, 23:06
Display posts from previous: Sort by

M20-26

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

Moderators: chetan2u, Bunuel

Events & Promotions

PREV
NEXT


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®.