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

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

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New post 01 Jun 2008, 05:50
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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 3 times the distance between m and 0.
(2) 12 is halfway between m and r.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-and-r-are-two-numbers-on-a-number-line-what-is-the-89018.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Apr 2012, 21:30, edited 1 time in total.
Edited the question and added the OA. Topic is locked.

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Re: If m and r are two numbers...DS [#permalink]

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New post 01 Jun 2008, 06:38
japped187 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 3 times the distance between m and 0.
(2) 12 is halfway between m and r.


Both (1) and (2) don't help!

"E"

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Re: If m and r are two numbers...DS [#permalink]

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New post 01 Jun 2008, 06:45
japped187 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 3 times the distance between m and 0.
(2) 12 is halfway between m and r.

E for me
Lets say distance between origin and m=x
so,between origin and r=3x
Distance between m and r= 3x-x = 2x or 3x+x=4x (depending on which side of 0 does r or m lie on )
1 is not enough
2 in itself is not enough
But if we use both
12 is half way between m and r
distance between m and r= 2x or 4x
so we cant say for sure.
E for me

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Re: If m and r are two numbers...DS [#permalink]

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New post 01 Jun 2008, 12:22
japped187 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 3 times the distance between m and 0.
(2) 12 is halfway between m and r.


I think the answer is C - the only solution is m = 6 , r = 18 to satisfy both.

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Re: If m and r are two numbers...DS [#permalink]

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New post 02 Jun 2008, 21:56
E.
Two solutions:
1.
r-0=3m-0
(m+r)/2=12
r=18, m=6
2.
0-r=3m-0
(m+r)/2=12
r=36, m=-12

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Re: If m and r are two numbers...DS [#permalink]

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New post 03 Jun 2008, 03:05
There are two possibilities .m an r could be on the same side of 0 or they can be different.
Since none of the choices makes this clear, not even by taking the two together. so i will also go with E.

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Re: If m and r are two numbers on a number line, what is the [#permalink]

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New post 26 Apr 2012, 20:40
can you guys go into more detail? i am still confused.
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Re: If m and r are two numbers on a number line, what is the [#permalink]

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New post 26 Apr 2012, 21:28
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calreg11 wrote:
can you guys go into more detail? i am still confused.


TIP:
On the GMAT we can often see such statement: \(k\) is halfway between \(m\) and \(n\) on the number line. Remember this statement can ALWAYS be expressed as:

\(\frac{m+n}{2}=k\).

Also on the GMAT when we see the distance between x and y, this can be expressed as \(|x-y|\).

Back to the question:
If m and r are two numbers on a number line, what is the value of r?

(1) The distance between r and zero is 3 times the distance between m and zero --> \(|r-0|=3|m-0|\) --> \(|r|=3|m|\) --> \(r=3m\) OR \(r=-3m\). Clearly insufficient.

(2) 12 is halfway between m and r --> \(\frac{r+m}{2}=12\) --> \(r+m=24\). Clearly insufficient.

(1)+(2) \(r=3m\) OR \(r=-3m\) and \(r+m=24\).

\(r=3m\) --> \(r+m=3m+m=24\) --> \(m=6\) and \(r=18\)
OR
\(r=-3m\) --> \(r+m=-3m+m=24\) --> \(m=-12\) and \(r=36\)

Two different values for \(r\). Not sufficient.

Answer: E.

In case of any question please post it here: if-m-and-r-are-two-numbers-on-a-number-line-what-is-the-89018.html
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Re: If m and r are two numbers on a number line, what is the   [#permalink] 26 Apr 2012, 21:28
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