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

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Manager
Joined: 07 May 2013
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Re: If m and r are two numbers on a number line, what is the [#permalink]

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04 Jun 2014, 20:16
Buneul, I did not understand why you took the case r=-3m.

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

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05 Jun 2014, 01:30
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Buneul, I did not understand why you took the case r=-3m.

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

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07 Mar 2016, 12:21
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1) m=6; r=18
2) m=-12; r=36

Not sufficient,

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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13 Nov 2016, 18:54
Bunuel wrote:
TooLong150 wrote:
Bunuel wrote:
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.

Bunuel, can you explain how $$|r|=3|m|$$ --> $$r=3m$$ OR $$r=-3m$$?

$$|r|=3|m|$$ means that the distance from r to 0 is thrice the distance from m to 0:

-----0--m-----r------
r-----m--0--------------

--m--0--------r------
r--------0--m------------

If r and m have the same sign (cases A and B), then r=3m but if r and m have different signs (cases C and D), then r=-3m.

Hope it's clear.

Hi Buenel,

I looked into your solution and noticed many are saying there is only 2 solutions hence insufficient. But just to fully understand this problem, isn't there more than 2 solutions?

For instance:

r could be - or +, m could be the opposite sign of r (- or +), or they both can be negative. Therefore multiple solutions? Or, am I missing something. I understand you wrote |r| = 3|m| -> r = 3m or r=-3m, however, could we also have -r = 3m?

Thank you

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

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07 Oct 2017, 22:43
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Re: If m and r are two numbers on a number line, what is the   [#permalink] 07 Oct 2017, 22:43

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