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

It is currently 21 Oct 2019, 01:11

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

If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Retired Moderator
avatar
Joined: 29 Oct 2013
Posts: 249
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
GMAT ToolKit User
If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

Show Tags

New post Updated on: 17 Jan 2019, 00:06
3
10
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:31) correct 21% (02:06) wrong based on 287 sessions

HideShow timer Statistics

If \(x\neq{-1}\) , \(\frac{1- x^{16}}{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)}\) is equivalent to

A. -1
B. 1
C. x
D. 1-x
E. x-1

_________________
Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Originally posted by NoHalfMeasures on 06 Jun 2014, 03:03.
Last edited by Bunuel on 17 Jan 2019, 00:06, edited 5 times in total.
Most Helpful Community Reply
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

Show Tags

New post 06 Jun 2014, 03:43
8
3
Bunuel, Thanks for the correction :)

Answer = D

Numerator

\(1 - x^{16}\)

\(= (1 + x^8) (1 - x^8)\)

\(= (1 + x^8) (1 + x^4) (1 - x^4)\)

\(= (1 + x^8) (1 + x^4) (1 + x^2) (1 - x^2)\)

\(= (1 + x^8) (1 + x^4) (1 + x^2) (1 + x) (1 - x)\)

Denominator

\((1 + x^8) (1 + x^4) (1 + x^2) (1 + x)\)


Expanded / simplified equation would be

\(\frac{(1 + x^8) (1 + x^4) (1 + x^2) (1 + x) (1 - x)}{(1 + x^8) (1 + x^4) (1 + x^2) (1 + x)}\)


= 1 - x

Answer = D
_________________
Kindly press "+1 Kudos" to appreciate :)
General Discussion
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

Show Tags

New post 06 Jun 2014, 03:28
1
Is this the value we require to find? Kindly confirm


\(1 - \frac{x^{16}}{(1+x)(1+x^2)(1+x^4)(1+x^8)}\)
_________________
Kindly press "+1 Kudos" to appreciate :)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58413
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

Show Tags

New post 06 Jun 2014, 03:31
2
Intern
Intern
User avatar
S
Joined: 05 Oct 2017
Posts: 45
Location: Bangladesh
Concentration: Accounting, Social Entrepreneurship
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

Show Tags

New post 17 Jan 2019, 00:03
NoHalfMeasures wrote:
If \(x\neq{-1}\) , \(\frac{1- x^{16}}{{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)}\) is equivalent to

A. -1
B. 1
C. x
D. 1-x
E. x-1


how to pick number in this question? Bunuel
_________________
.... You are already NAKED. There is NO reason not to FOLLOW your heart.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58413
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

Show Tags

New post 17 Jan 2019, 00:12
1
rashedBhai wrote:
NoHalfMeasures wrote:
If \(x\neq{-1}\) , \(\frac{1- x^{16}}{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)}\) is equivalent to


A. -1
B. 1
C. x
D. 1-x
E. x-1


how to pick number in this question? Bunuel


Pick x = 1. In this case the numerator is 0, thus the whole fraction is 0. Now, plug x = 1 into the options to check which of them give 0. Only D and E fit.

Now, pick x = 2. In this case the numerator is negative and the denominator is positive, thus the whole fraction is negative. Out of D and E, only D is negative if x = 2.


Answer: D.
_________________
Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

Show Tags

New post 17 Jan 2019, 00:25
NoHalfMeasures wrote:
If \(x\neq{-1}\) , \(\frac{1- x^{16}}{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)}\) is equivalent to

A. -1
B. 1
C. x
D. 1-x
E. x-1


A question in which basic formula works a^2 - b^2 = (a-b) (a+b)

Now you can expand the numerator as

1-x^16 = (1-x) (1+x) (1+x^2) (1+x^4) (1 + x^8)

Which will result in Answer D
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
GMAT Club Bot
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)   [#permalink] 17 Jan 2019, 00:25
Display posts from previous: Sort by

If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne