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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which if the following has a root in common with x^2 - 6x + 5 = 0

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

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Difficulty:   35% (medium)

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

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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  S
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GMAT 1: 600 Q48 V25
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Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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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 V
Joined: 22 May 2016
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Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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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.

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

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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

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

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Option D has the root x = 1 common with the equation given in stimulus.
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Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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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.

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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

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