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# Which of the following sets includes ALL of the solutions of

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GMAT Instructor
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Which of the following sets includes ALL of the solutions of  [#permalink]

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16 Jul 2003, 01:02
00:00

Difficulty:

(N/A)

Question Stats:

50% (02:23) correct 50% (01:02) wrong based on 14 sessions

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Which of the following sets includes ALL of the solutions of x that will satisfy the equation:

|x тАУ 2| - |x тАУ 3| = |x тАУ 5|?

(A) {-6, -5, 0, 1, 7, 8}
(B) {-4, -2, 0, 10/3, 4, 5}
(C) {-4, 0, 1, 4, 5, 6}
(D) {-1, 10/3, 3, 5, 6, 8}
(E) {-2, -1, 1, 3, 4, 5}

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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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16 Jul 2003, 02:10
D.
Simple, but effective way - I found that 6 is the solution. so, I eliminated wrong answers. then I tryed 0 in the remaining ones and ended up this D.
GMAT Instructor
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16 Jul 2003, 02:35
Any more tries?

_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

SVP
Joined: 03 Feb 2003
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16 Jul 2003, 03:17
1
I have just solved the equation and got only 4 and 6.
Manager
Joined: 08 Apr 2003
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16 Jul 2003, 03:19
Ans is C.

Take 2 < x < 3.

So the equation will be,

x -2 +x -3 = -x +5.

So, 3x = 10.

So, x = 10/3 not possible.

Take 3 < x < 5
x =4,

Take x >5

So x = 6.
GMAT Instructor
Joined: 07 Jul 2003
Posts: 740
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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16 Jul 2003, 03:41
evensflow wrote:
Ans is C.

Take 2 < x < 3.

So the equation will be,

x -2 +x -3 = -x +5.

So, 3x = 10.

So, x = 10/3 not possible.

Take 3 < x < 5
x =4,

Take x >5

So x = 6.

Your solution has the proper approach. You forgot to check x<2, but there is no solution in that interval so your answer is correct.

BTW, I composed the problem this way so that it would be somewhat timeconsuming to backsolve it (i.e., check all the answers).
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Manager
Joined: 08 Apr 2003
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16 Jul 2003, 03:51
Well i did for x <2 also on paper..

but felt lazy to type the answer as yes the soultion is not possible, since x = 6.
Manager
Joined: 03 Jun 2003
Posts: 80
Location: Uruguay

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16 Jul 2003, 11:14
Sorry, I don┬┤t get it

In C, you have number 0, and that does not satisfy the equation, how can be right?
GMAT Instructor
Joined: 07 Jul 2003
Posts: 740
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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16 Jul 2003, 12:34
MBA04 wrote:
Sorry, I don┬┤t get it

In C, you have number 0, and that does not satisfy the equation, how can e right?

I asked for the set that contained all of the solutions, not the set where egvery member was a solution. The only solutions are 4 and 6. C has both of them.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Senior Manager
Joined: 11 Nov 2003
Posts: 346
Location: Illinois

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12 Feb 2004, 15:04
evensflow wrote:
Ans is C.

Take 2 < x < 3.

So the equation will be,

x -2 +x -3 = -x +5.

So, 3x = 10.

So, x = 10/3 not possible.

Take 3 < x < 5
x =4,

Take x >5

So x = 6.

Hi Akamai,

In the above approach, while selecting various range, should we consider one of the extreme as part of the range? For exampl, instead of range x > 5, should we consider x >= 5. So that just in case if we arrive at x = 5 then that can be considered valid solution? I know it is not applicable in this problem but what if the quation is designed that way?

Thanks
GMAT Instructor
Joined: 07 Jul 2003
Posts: 740
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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14 Feb 2004, 01:34
If the solution is right on the value, then it will be a valid solution in both intervals (before and after) so >= is fine unless the variable is in the denominator and will equal zero.

--== 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.

_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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23 Jan 2019, 06:37
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Re: Which of the following sets includes ALL of the solutions of   [#permalink] 23 Jan 2019, 06:37
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