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

It is currently 22 Jan 2019, 15:16

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
  • 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.
  • Key Strategies to Master GMAT SC

     January 26, 2019

     January 26, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?

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

Hide Tags

 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6826
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post Updated on: 16 Nov 2016, 22:51
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:04) correct 31% (02:53) wrong based on 131 sessions

HideShow timer Statistics

If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?

A. ±1/√2
B. ±1
C. ±√2
D. ±√3
E. ±2

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"


Originally posted by MathRevolution on 29 Sep 2016, 05:23.
Last edited by MathRevolution on 16 Nov 2016, 22:51, edited 2 times in total.
Current Student
avatar
B
Joined: 24 Jul 2016
Posts: 80
Location: United States (MI)
GMAT 1: 730 Q51 V40
GPA: 3.6
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 30 Sep 2016, 02:53
Answer is C. N can be +2 or -2. What's the OA?


Sent from my iPhone using GMAT Club Forum mobile app
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6826
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 01 Oct 2016, 01:06
==>If you substitute x=1, from 1^6+1=(1+n+1)(1-n+1), you get 2=(2+n)(2-n)=4-n^2. Naturally, you get n^2=4-2=2, and n=±√2. Therefore the answer is C.

Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
avatar
B
Joined: 29 Dec 2014
Posts: 67
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 15 Nov 2016, 07:44
MathRevolution wrote:
==>If you substitute x=1, from 1^6+1=(1+n+1)(1-n+1), you get 2=(2+n)(2-n)=4-n^2. Naturally, you get n^2=4-2=2, and n=±√2. Therefore the answer is C.

Answer: C


Hi, please can you show how to solve it alegebraically?

Thanks
Intern
Intern
avatar
B
Joined: 29 Jun 2016
Posts: 6
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 15 Nov 2016, 08:35
given :x^6 + 1= (x^3+nx+1)(x^3-nx+1)
solve RHS:
[(x^3+1)+nx][(x^3+1)-nx]

by using (a+b)(a-b)=a^2-b^2

we have: a= (x^3+1) and b = nx

after solving we get: (x^3+1)^2 - (nx)^2
x^6+1+2x^3-(nx)^2
but on LHS we have x^6+1 so on RHS remaining terms should be zero. i.e. 2x^3 - (nx)^2 = 0.

so what should be next ? can any one tell me ?
Intern
Intern
avatar
B
Joined: 29 Jun 2016
Posts: 6
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 15 Nov 2016, 08:48
guys please see my solution and put the given answer (underroot 2) in final equation:
x^6 +1 + 2x^3 - 2x^2.
so for RHS to be equal to LHS there should be 2x^2 instead of 2x^3. so i think that there is some mistake in question.
Retired Moderator
User avatar
V
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 988
Location: India
GPA: 3.64
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 15 Nov 2016, 08:58
3
1
WilDThiNg wrote:
MathRevolution wrote:
==>If you substitute x=1, from 1^6+1=(1+n+1)(1-n+1), you get 2=(2+n)(2-n)=4-n^2. Naturally, you get n^2=4-2=2, and n=±√2. Therefore the answer is C.

Answer: C


Hi, please can you show how to solve it alegebraically?

Thanks


Solving the Right hand side which is \((x^3+nx+1)(x^3-nx+1) = (x^3+1)^2 - (nx)^2\) ---using the formula \((a+b)(a-b)= a^2-b^2\)
equal to , \(x^6+1+2x^3-n^2x^2\)
equating LHS=RHS
\(x^6+1=x^6+1+2x^3-n^2x^2\)
gives \(2x^3-n^2x^2=0\)
therefore \(n^2=2x\)
n=\(±\sqrt{2x}\)
When x=0, n=0
when x=1, n=\(±\sqrt{2}\) which is option C

If u found my post useful, press kudos!
_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Manager
Manager
avatar
B
Joined: 29 Dec 2014
Posts: 67
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 15 Nov 2016, 14:37
souvonik2k: Thank you!
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6826
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 16 Nov 2016, 22:52
Hi all,

We have revised the question.
Sorry about the confusion.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Director
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 533
Location: India
Premium Member
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?  [#permalink]

Show Tags

New post 27 Feb 2017, 04:08
Substitute x = 1 in the equation. We will have
1^6+1=(1^3+n+1)(1^3-n+1)
Or (2+n)(2-n) = 2
Or 4-n^2 = 2
Or n = ±√2
_________________

GMAT Mentors
Image

GMAT Club Bot
Re: If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=? &nbs [#permalink] 27 Feb 2017, 04:08
Display posts from previous: Sort by

If (x^4)+1=(x^2+nx+1)(x^2-nx+1), n=?

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


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®.