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

It is currently 14 Oct 2019, 21:05

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

Which of the following equations has a root in common with x^2−6x+8=0

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58323
Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 18 Nov 2016, 03:55
1
2
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (01:43) correct 34% (01:35) wrong based on 228 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2016
Posts: 256
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 18 Nov 2016, 04:37
Bunuel wrote:
Which of the following equations has a root in common with \(x^2−6x+8=0\)?

A. \(x^2+x−2=0\)

B. \(x^2+4=0\)

C. \(x^2−12x+16=0\)

D. \(32−2x^2=0\)

E. \(x^2−4x+16=0\)


x^2-6x+8=0 can be factorized as (x-2) (x-4)

A. \(x^2+x−2=0\) can be factorized as (x+2) (x-1)

B. \(x^2+4=0\) can be factorized as x^2= -4 imaginary roots

C. \(x^2−12x+16=0\) can be fctorized as x= (6+ 2(sqrt 5)), (6- 2(sqrt 5))

D. \(32−2x^2=0\) can be factorized as x= 4, -4 shares a common root with x^2-6x+8=0

E. \(x^2−4x+16=0\) can be factorized to get imaginary roots

Hence D
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4765
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 18 Nov 2016, 09:30
1
1
Bunuel wrote:
Which of the following equations has a root in common with \(x^2−6x+8=0\)?

A. \(x^2+x−2=0\)

B. \(x^2+4=0\)

C. \(x^2−12x+16=0\)

D. \(32−2x^2=0\)

E. \(x^2−4x+16=0\)


\(x^2−6x+8=0\)

Or, \(x^2−4x −2x +8=0\)

Or, \(x ( x − 4) −2 ( x − 4 ) = 0\)

So, x = 2 , 4

Check the options using x = 2 & 4..

Except (D) , none satisfies ..

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4000
Location: Canada
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 18 Nov 2016, 09:43
Top Contributor
Bunuel wrote:
Which of the following equations has a root in common with \(x^2−6x+8=0\)?

A. \(x^2+x−2=0\)

B. \(x^2+4=0\)

C. \(x^2−12x+16=0\)

D. \(32−2x^2=0\)

E. \(x^2−4x+16=0\)


The solutions provided in the above posts are great, so I won't provide another solution that's similar.

However, I'd like to point out this this is one of those questions that require us to check/test each answer choice. That is, once we find the solutions to the given quadratic equation, we must then solve the equation in each answer choice until we find one that has a matching solution.
In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article: http://www.gmatprepnow.com/articles/han ... -questions

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 29 Nov 2016, 15:57
1
2
Bunuel wrote:
Which of the following equations has a root in common with \(x^2−6x+8=0\)?

A. \(x^2+x−2=0\)

B. \(x^2+4=0\)

C. \(x^2−12x+16=0\)

D. \(32−2x^2=0\)

E. \(x^2−4x+16=0\)


We can start by factoring the given equation of x^2 - 6x + 8 = 0:

(x - 4)(x - 2) = 0

x = 4 or x = 2

Now let’s analyze each answer choice to determine which has a root in common with x^2 - 6x + 8 = 0.

A) x^2 + x - 2 = 0

(x + 2)(x - 1) = 0

x = -2 or x = 1

Answer choice A DOES NOT have a root in common with x^2 - 6x + 8 = 0.

B) x^2 + 4 = 0

Since x^2 + 4 = 0 cannot be factored (over the real numbers), answer choice B DOES NOT have a root in common with x^2 - 6x + 8 = 0.

C) x^2 - 12x + 16 = 0

Since x^2 - 12x + 16 = 0 cannot be factored (over the integers), answer choice C DOES NOT have a root in common with x^2 - 6x + 8 = 0.

D) 32 - 2x^2 = 0

2(16 - x^2) = 0

2(4 + x)(4 - x) = 0

x = -4 or x = 4

Answer choice D DOES have a root in common with x^2 - 6x + 8 = 0.

E) x^2 - 4x + 16 = 0

Since x^2 - 4x + 16 = 0 cannot be factored (over the real numbers), answer choice E DOES NOT have a root in common with x^2 - 6x + 8 = 0.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior Manager
Senior Manager
User avatar
S
Joined: 08 Dec 2015
Posts: 285
GMAT 1: 600 Q44 V27
Reviews Badge
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 29 Jan 2017, 05:53
Hi everyone!

Can please someone tell me where i can find how to solve these questions with quadratics quickly?

I start by doing the "what can be multiplied to give C and summed to give B" method. But it takes a lot of time!

What do I need to know of shortcuts here?

Thank you!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58323
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 29 Jan 2017, 10:16
iliavko wrote:
Hi everyone!

Can please someone tell me where i can find how to solve these questions with quadratics quickly?

I start by doing the "what can be multiplied to give C and summed to give B" method. But it takes a lot of time!

What do I need to know of shortcuts here?

Thank you!


Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm
Solving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm
_________________
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4765
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 29 Jan 2017, 10:46
iliavko wrote:
Hi everyone!

Can please someone tell me where i can find how to solve these questions with quadratics quickly?

I start by doing the "what can be multiplied to give C and summed to give B" method. But it takes a lot of time!

What do I need to know of shortcuts here?

Thank you!


Bunuel has already provided the links the formula for solving any Quad Equation is as below -
Attachment:
qform01.gif
qform01.gif [ 690 Bytes | Viewed 1879 times ]


http://www.purplemath.com/modules/solvquad4.htm

Hope this helps...
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Intern
avatar
B
Joined: 11 Oct 2016
Posts: 3
Location: Canada
GMAT ToolKit User
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 30 Jan 2017, 08:57
1
You can plug in roots of equation x^2-6x+8=0 (which are 4 & 2 ) in a, b, c, d, e equations:
A. x^2+x−2=0
plug in 2→2^2+2-2≠0
plug in 4→4^2+4-2≠0

B. x^2+4=0
plug in 2→2^2+4≠0
plug in 4→4^2+4≠0

C. x^2−12x+16=0
plug in 2→2^2-12*2+16*2≠0
plug in 4→4^2-12*4+16≠0

D. 32−2x^2=0
plug in 2→32-2*2^2≠0
plug in 4→32-2*4^2=32-2*16=32-32=0 CHECK;4 IS ONE ROOT IN COMMUN!

E. x2−4x+16=0
plug in 2→2^2-4*2+16≠0
plug in 4→4^2-4*4+16≠0

hope this helps!
Intern
Intern
avatar
B
Joined: 28 Jan 2017
Posts: 49
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 29 May 2017, 03:17
Bunuel wrote:
Which of the following equations has a root in common with \(x^2−6x+8=0\)?

A. \(x^2+x−2=0\)

B. \(x^2+4=0\)

C. \(x^2−12x+16=0\)

D. \(32−2x^2=0\)

E. \(x^2−4x+16=0\)


Hi Bunuel,

I chose the correct answer but on the basis of most of the answer choice produce complex numbers as the root of the equation. However, I have seen here that people are considering only the real number as the root of the equations.

Does GMAT test complex numbers, or I am overthinking.

Please suggest.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58323
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 29 May 2017, 03:21
ravi11 wrote:
Bunuel wrote:
Which of the following equations has a root in common with \(x^2−6x+8=0\)?

A. \(x^2+x−2=0\)

B. \(x^2+4=0\)

C. \(x^2−12x+16=0\)

D. \(32−2x^2=0\)

E. \(x^2−4x+16=0\)


Hi Bunuel,

I chose the correct answer but on the basis of most of the answer choice produce complex numbers as the root of the equation. However, I have seen here that people are considering only the real number as the root of the equations.

Does GMAT test complex numbers, or I am overthinking.

Please suggest.


All numbers on the GMAT are by default real numbers.
_________________
Senior Manager
Senior Manager
User avatar
S
Joined: 12 Sep 2017
Posts: 301
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

Show Tags

New post 07 Mar 2019, 20:54
Vinayak Shenoy wrote:
Bunuel wrote:
Which of the following equations has a root in common with \(x^2−6x+8=0\)?

A. \(x^2+x−2=0\)

B. \(x^2+4=0\)

C. \(x^2−12x+16=0\)

D. \(32−2x^2=0\)

E. \(x^2−4x+16=0\)


x^2-6x+8=0 can be factorized as (x-2) (x-4)

A. \(x^2+x−2=0\) can be factorized as (x+2) (x-1)

B. \(x^2+4=0\) can be factorized as x^2= -4 imaginary roots

C. \(x^2−12x+16=0\) can be fctorized as x= (6+ 2(sqrt 5)), (6- 2(sqrt 5))

D. \(32−2x^2=0\) can be factorized as x= 4, -4 shares a common root with x^2-6x+8=0

E. \(x^2−4x+16=0\) can be factorized to get imaginary roots

Hence D


VINAYAK Shenoy

Could you please explain how to factorize C?

Kind regards!
GMAT Club Bot
Re: Which of the following equations has a root in common with x^2−6x+8=0   [#permalink] 07 Mar 2019, 20:54
Display posts from previous: Sort by

Which of the following equations has a root in common with x^2−6x+8=0

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





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