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

[SummerCourse]

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

[dbernst]

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

[SummerCourse]

Dan,

Thanks for the explanation. I apprecaite your help.

[perez.analuisa]

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

[RonPurewal]

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.

[Jazmet]

Hi Dan,

Please help. How did you come up with r = -3m?

I know about r = 3m and this is how I figured -

r- 0 = 3(m - 0) / r = 3m

[RonPurewal]

Hi Dan,

Please help. How did you come up with r = -3m?

I know about r = 3m and this is how I figured -

r- 0 = 3(m - 0) / r = 3m

Dan B hasn't posted on these forums in almost six years. Heh. Check the timestamp before you address the specific writer of a post -- if you're responding to a post from 2007, it's unlikely that the original author will respond. (:

"the distance between 0 and r" doesn't have to be r - 0. If r is less than 0, it's 0 - r.
Same with the other distance, which could be m - 0, but could also be 0 - m.

Try these combinations and you'll see what's up.

[Jazmet]

Alright, I got it now. Thanks Ron.

And I really didn't notice that the post was 6 years old. Will take care of it in future.

[RonPurewal]

No worries