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

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SummerCourse
 Post subject: If m and r are two numbers on a number line, what is
 Post Posted: Tue Sep 04, 2007 10:57 pm 
Any input on some good numbers that can be used to solve this problem? I used various integers (which I assume may be my error) and found that only m=6 and n=18 work. Can someone help explain where my logic is incorrect?

Thanks


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dbernst
 Post subject:
 Post Posted: Thu Sep 06, 2007 12:31 pm 
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ManhattanGMAT Staff


Posts: 304
SummerCourse, since the natural instinct is to try only positive values for m and r, this is a very tricky problem.

Statement (1) tells us that r = 3m or r = -3m (as either case would result in an r with an absolute value that is three times that of m). Insufficient. Eliminate AD from AD/BCE Grid.

Statement (2) tells us that (r+m)/2 = 12. Insufficient. Eliminate B from remaining BCE Grid.

By substituting each equation from Statement (1) into the equation from Statement (2), the statements together tell us that 3m + m = 24, so m = 6 and r = 18, or that -3m + m = 24, so m = -12 and r = 36. As there are still two possible values for r, the correct answer is E.

Hope that helps!
-dan
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SummerCourse
 Post subject:
 Post Posted: Thu Sep 06, 2007 5:29 pm 
Dan,

Thanks for the explanation. I apprecaite your help.
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perez.analuisa
 Post subject: Re: If m and r are two numbers on a number line, what is
 Post Posted: Sun Nov 15, 2009 4:24 am 
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Prospective Students


Posts: 1
Dan,
Could the values also be: m = -6 and r = -18 or m = 12 and r = -36?
Thanks.
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RonPurewal
 Post subject: Re: If m and r are two numbers on a number line, what is
 Post Posted: Fri Dec 18, 2009 5:41 am 
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ManhattanGMAT Staff


Posts: 7146
perez.analuisa wrote:
Dan,
Could the values also be: m = -6 and r = -18 or m = 12 and r = -36?
Thanks.


nope. the point halfway between these pairs of numbers is -12, not 12. therefore, these points don't satisfy the second statement.
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