GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Jul 2020, 19:11

### 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

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

# Which if the following has a root in common with x^2 - 6x + 5 = 0

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 May 2018
Posts: 7
Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

### Show Tags

22 May 2018, 17:25
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:31) correct 31% (01:57) wrong based on 101 sessions

### HideShow timer Statistics

Which if the following has a root in common with x^2 - 6x + 5 = 0

A. x^2+ 1 = 0

B. x^2 - x-2 = 0

C. x^2 - 10x - 5 = 0

D. 2x^2 - 2 = 0

E. x^2 - 2x-3 = 0
Manager
Joined: 22 Jun 2017
Posts: 64
Location: Brazil
GMAT 1: 600 Q48 V25
GPA: 3.5
WE: Engineering (Energy and Utilities)
Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

### Show Tags

22 May 2018, 18:35
2
1
Option D

$$x^2-6x+5$$ = $$(x-5)$$$$(x-1)$$

roots = 5 or 1

- now check/test each answer choice using x = 1 and x = 5 (In these situations, always check the answer choices from E to A: https://www.gmatprepnow.com/articles/handling-%E2%80%9Canalyze-answer-choices%E2%80%9D-questions)

Only D satisfies.
Senior SC Moderator
Joined: 22 May 2016
Posts: 3938
Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

### Show Tags

23 May 2018, 07:05
2
Abhimanyu111 wrote:
Which if the following has a root in common with x^2 - 6x + 5 = 0

A. x^2+ 1 = 0

B. x^2 - x-2 = 0

C. x^2 - 10x - 5 = 0

D. 2x^2 - 2 = 0

E. x^2 - 2x-3 = 0

Factor the quadratic to find its roots
$$x^2 - 6x + 5 = 0$$
$$(x - 1)(x - 5)= 0$$
$$x = 1$$ or $$x = 5$$

Plug both roots into the answer choices. Scan the choices first.

Eliminate A (inevitable positive result, not 0); and
Eliminate C (with roots this small, inevitable negative result).*

The arithmetic here is easy. I started with B. This question took a little over half a minute.
Analysis of all choices for those who are curious:

A. $$x^2+ 1 = 0$$
$$x=1$$: $$(1+1) = 2$$ NO
$$x=5$$: $$(25+1)=26$$ NO

B. $$x^2 - x-2 = 0$$
$$x=1$$: $$(1-1-2) = -2$$ NO
$$x=5$$: $$(25-5-2) = 18$$ NO

C. $$x^2 - 10x - 5 = 0$$
$$x=1$$: $$(1-10-5) = -14$$
$$x=5$$: $$(25-50-5) = -30$$

D. $$2x^2 - 2 = 0$$
$$x=1$$: $$(2-2) = 0$$ YES
Finished. We just need one root.

In case there is doubt, (D) cont.:
$$x=5$$: $$(50-2=48)$$ NO. Does not matter. We need "a" root (one) in common. We have $$x = 1$$

E. $$x^2 - 2x-3 = 0$$
$$x=1$$: $$(1-2-3) = -4$$
$$x=5$$: $$(25-10-3) = 12$$ NO

*Eliminate A: Both roots are positive. Answer A has two positive terms and a plus sign. Positive roots cannot make that equation true.
Eliminate C: For roots 1 and 5, the squared $$a$$ term is not great enough to overcome the negative coefficient of the $$b$$ term
** FillFM links to an excellent article that recommends starting with E for "analyze the answer choices". (The stats are startling.) I'm a bit paranoid. GMAC adapts to public warnings.

_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.

BLACK LIVES MATTER.
Director
Joined: 02 Oct 2017
Posts: 678
Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

### Show Tags

20 Jun 2018, 08:11
x^2 - 6x + 5 = 0
Has two roots
(x-1)(x-5)=0
X=1,5

And 1 is root of choice D
i.e. 2(x^2-1)=0
2(x+1)(x-1)=0
X=1,-1

Give kudos if it helps

Posted from my mobile device
VP
Joined: 11 Feb 2015
Posts: 1173
Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

### Show Tags

20 Jun 2018, 08:24
Option D has the root x = 1 common with the equation given in stimulus.
_________________
Manish
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11036
Location: United States (CA)
Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

### Show Tags

21 Jun 2018, 15:56
Abhimanyu111 wrote:
Which if the following has a root in common with x^2 - 6x + 5 = 0

A. x^2+ 1 = 0

B. x^2 - x-2 = 0

C. x^2 - 10x - 5 = 0

D. 2x^2 - 2 = 0

E. x^2 - 2x-3 = 0

Simplifying the given equation, we have:

x^2 - 6x + 5 = 0

(x - 5)(x - 1) = 0

x = 5 or x = 1

By scanning through the answer choices, we see x = 1 is a solution to 2x^2 - 2 = 0. Thus, choice D is the answer.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 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

Re: Which if the following has a root in common with x^2 - 6x + 5 = 0   [#permalink] 21 Jun 2018, 15:56