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# If m and r are two numbers on a number line, what is the

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Manager
Joined: 19 Oct 2008
Posts: 91
If m and r are two numbers on a number line, what is the [#permalink]

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18 Mar 2009, 18:24
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If m and r are two numbers on a number line, what is the value of r?

1) The distance between r and 0 is three times the distance between m and 0.
2) 12 is halfway between m and r
Intern
Joined: 16 Mar 2009
Posts: 26
Re: Numbers on number line GMAT Prep PB [#permalink]

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18 Mar 2009, 18:44
r = 3m
r - 12 = 12 - m => r + m = 24

we can solve if substitute eq1 into eq2
4m=24 => m=6 hence r=18

so "can solve if BOTH taken together " ans is C
Director
Joined: 14 Aug 2007
Posts: 704
Re: Numbers on number line GMAT Prep PB [#permalink]

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18 Mar 2009, 19:18
Accountant wrote:
If m and r are two numbers on a number line, what is the value of r?

1) The distance between r and 0 is three times the distance between m and 0.
2) 12 is halfway between m and r

E.

1) talks about "distance" i.e absolute value => |r|=3*|m| 2 cases r=3m OR r=-3m

so together with 2) results in 2 solutions.
Intern
Joined: 16 Mar 2009
Posts: 26
Re: Numbers on number line GMAT Prep PB [#permalink]

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18 Mar 2009, 20:26
@alpha_plus_gamma

@Accountant
What is the OA ?
VP
Joined: 18 May 2008
Posts: 1205
Re: Numbers on number line GMAT Prep PB [#permalink]

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18 Mar 2009, 23:41
will go with the reasoning of alpha_plus_gamma
Definitely E
Manager
Joined: 19 Oct 2008
Posts: 91
Re: Numbers on number line GMAT Prep PB [#permalink]

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19 Mar 2009, 05:29
OA is E, can you plug in some numbers and prove that both statements taken together give two or more answers. I only got one answer when I plug in numbers which statisfy both statements:
m=6
r=18

I couldn't find any other values which satisfied both statements since twleve has to be halfway between them. I am sure I am missing something here.
Manager
Joined: 19 Oct 2008
Posts: 91
Re: Numbers on number line GMAT Prep PB [#permalink]

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19 Mar 2009, 05:29
OA is E, can you plug in some numbers and prove that both statements taken together give two or more answers. I only got one answer when I plug in numbers which statisfy both statements:
m=6
r=18

I couldn't find any other values which satisfied both statements since twleve has to be halfway between them. I am sure I am missing something here.
Director
Joined: 29 Aug 2005
Posts: 836
Re: Numbers on number line GMAT Prep PB [#permalink]

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14 Apr 2009, 00:06
Stmt1: |r|=3|m| i.e. r=3m OR r=-3m
Stmt2: r+m=24

Neither is sufficient by itself.

Together: r+m=24. Substitute this into r=3m and r=-3m.
This will yield r=36, m=-12; and r=18, m=6

Two possible values for r. So, E.

Last edited by seofah on 09 Jun 2009, 09:02, edited 1 time in total.
Manager
Joined: 22 Feb 2009
Posts: 135
Schools: Kellogg (R1 Dinged),Cornell (R2), Emory(Interview Scheduled), IESE (R1 Interviewed), ISB (Interviewed), LBS (R2), Vanderbilt (R3 Interviewed)
Re: Numbers on number line GMAT Prep PB [#permalink]

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14 Apr 2009, 09:19
Also is it treu that the value r could be an integer or a fraction. Nothing is mentioned on that. So i guess its E
Intern
Joined: 05 Jun 2007
Posts: 48
Schools: CMU, Ross, Kellogg, Case, OSU, Stanford, Kelley
Re: Numbers on number line GMAT Prep PB [#permalink]

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14 Apr 2009, 11:11
The ans has to be E.

Stmt 1 : r=3m or r=-3m ---> Not suff
Stmt 2: r+m=24 -----> Not suff

when we combine both the stmts
when r=3m ; m=6 & r=18
when r=-3m; m=-12 & r=36

As we get 2 values for r both stmts combined not suff.
Hence Ans is E
Manager
Joined: 19 Aug 2006
Posts: 233
Re: Numbers on number line GMAT Prep PB [#permalink]

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16 Apr 2009, 19:57
I also got E - combining does not help, as there could be many possible values for m and r.
Re: Numbers on number line GMAT Prep PB   [#permalink] 16 Apr 2009, 19:57
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