If m and r are two numbers on a number line, what is the : GMAT Data Sufficiency (DS)
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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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01 Jun 2008, 04:50
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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, 20:30, 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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01 Jun 2008, 05:38
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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01 Jun 2008, 05:45
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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01 Jun 2008, 11:22
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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02 Jun 2008, 20:56
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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03 Jun 2008, 02:05
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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26 Apr 2012, 19:40
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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26 Apr 2012, 20:28
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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, 20:28
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