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# What is the product of all the solutions of x^2 -4x+6= 3-|x-1|

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Intern
Joined: 09 Dec 2016
Posts: 1
What is the product of all the solutions of x^2 -4x+6= 3-|x-1|  [#permalink]

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23 May 2017, 06:37
00:00

Difficulty:

(N/A)

Question Stats:

67% (02:13) correct 33% (05:14) wrong based on 3 sessions

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What is the product of all the solutions of x^2 -4x+6= 3-|x-1|
A) -8
B) -4
C) -2
D) 4
E) 8

Hello I have an issue regarding this problem: (source Jeff Sackmann)

We have two options to consider:
1/ x-1 >= 0 that is x>=1
In this case we have two solutions x=2 or x=1
Both solutions are >=1

2/ x-1 <= 0 that is x<=1
In this case we also have two solutions x=1 or X=4
But in this case X=4 should be rejected since we have assumed that x<=1

So the products of all solutions should be 2*1*1=2

Or in the Jeff Sackmann book they considered valid the 4 solutions and then the answer is 8.

Thank you

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Math Expert
Joined: 02 Sep 2009
Posts: 49251
Re: What is the product of all the solutions of x^2 -4x+6= 3-|x-1|  [#permalink]

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23 May 2017, 06:39
Audrey92300 wrote:
What is the product of all the solutions of x^2 -4x+6= 3-|x-1|
A) -8
B) -4
C) -2
D) 4
E) 8

Hello I have an issue regarding this problem: (source Jeff Sackmann)

We have two options to consider:
1/ x-1 >= 0 that is x>=1
In this case we have two solutions x=2 or x=1
Both solutions are >=1

2/ x-1 <= 0 that is x<=1
In this case we also have two solutions x=1 or X=4
But in this case X=4 should be rejected since we have assumed that x<=1

So the products of all solutions should be 2*1*1=2

Or in the Jeff Sackmann book they considered valid the 4 solutions and then the answer is 8.

Thank you

Discussed here: what-is-the-product-of-all-the-solutions-of-x-2-4x-147152.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: What is the product of all the solutions of x^2 -4x+6= 3-|x-1| &nbs [#permalink] 23 May 2017, 06:39
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