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

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Manager
Joined: 21 Mar 2007
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If m and r are two numbers on a number line, what is the [#permalink]

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01 Jun 2008, 05:50
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95% (hard)

Question Stats:

47% (01:06) correct 53% (01:18) wrong based on 535 sessions

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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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Director
Joined: 03 Sep 2006
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Re: If m and r are two numbers...DS [#permalink]

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

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

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

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

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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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Manager
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Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)
Re: If m and r are two numbers on a number line, what is the [#permalink]

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26 Apr 2012, 20:40
can you guys go into more detail? i am still confused.
_________________

DETERMINED TO BREAK 700!!!

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

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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.

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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