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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]  18 Dec 2009, 15:27
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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.
[Reveal] Spoiler: OA

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Re: Number Line - DS [#permalink]  18 Dec 2009, 17:49
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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.

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Re: Number Line - DS [#permalink]  19 Dec 2009, 04:04
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xcusemeplz2009 wrote:
bth the statments are not suff...

s1) let m-0=x, then r-0=3x ( x can be 1,2,3,4,......anything)...not suff
s2) m-12=12-r or r-12=12-m....(can have any value)...not suff

s1)+s2)if m-12=1,2,3,4,5.... then 12-r=3,6,9,12,15...any thing
same for r-12...hence
from bth also we are not getting any particular value
so E

The answer is correct, but there is some problems in solution:

(1) When you write: m=x and r=3x, it's not right: if m=x, then r=3x OR r=-3x, as |r|=3|m|.

(2) You wrote: m-12=12-r or r-12=12-m. If you look at it you'll see that these two equations are the same and derived from \frac{m+r}{2}=12.

Again:
Statement: distance between r and x, is three times the distance between m and x can be expressed as |r-x|=3|m-x|.

Statement: k is halfway between m and r on the number line can be expressed as:

\frac{m+r}{2}=k.
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Re: Number Line - DS [#permalink]  19 Dec 2009, 08:29
thanks Bunuel for the clear analysis. Kudos to you
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Re: Number Line - DS [#permalink]  20 Dec 2009, 05:28
Bunuel wrote:
xcusemeplz2009 wrote:
bth the statments are not suff...

s1) let m-0=x, then r-0=3x ( x can be 1,2,3,4,......anything)...not suff
s2) m-12=12-r or r-12=12-m....(can have any value)...not suff

s1)+s2)if m-12=1,2,3,4,5.... then 12-r=3,6,9,12,15...any thing
same for r-12...hence
from bth also we are not getting any particular value
so E

The answer is correct, but there is some problems in solution:

(1) When you write: m=x and r=3x, it's not right: if m=x, then r=3x OR r=-3x, as |r|=3|m|.

(2) You wrote: m-12=12-r or r-12=12-m. If you look at it you'll see that these two equations are the same and derived from \frac{m+r}{2}=12.

Again:
Statement: distance between r and x, is three times the distance between m and x can be expressed as |r-x|=3|m-x|.

Statement: k is halfway between m and r on the number line can be expressed as:

\frac{m+r}{2}=k.

thanks bunuel
i cud not express it in a correct manner , but my intention was same since i tried on no. line and i got it in a easier way ,however cudn't express that in my post(appologies for that), on a no. line it was clear that the position of m and r is not fix with bth the given information hence insuff....
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Re: GMAT Prep [#permalink]  07 Jan 2010, 12:49
IMO ... E..

Question: wat is r?

ST1: The distance between r and 0 is 3 times the distance between m and 0
Since the statement has the term 'distance' in it, it signifies that we are not consider the -ve or +ve possibility of the number position.
Hence ST1 can be written algebrically as:
|r-0| = 3|m-0| ---> |r| = 3|m|
Clearly NOT SUFF as m could be anything and even if m is constant, r could be -3m or 3m

ST2: 12 is halfway between m & r is clearly NOT SUFF as the same is true for (m=11,r = 13) , (m=10,r = 14)....

Both ST1 and ST2 together would give us:
m = 6 and r = 18, m=-12 & r = 36 ...etc..Hence NOT SUFF....

OA as D.... ... Not sure..
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Re: Distance between two points - Gmatprep [#permalink]  04 Jan 2012, 06:33
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Janealams wrote:
Can somebody explain this to me please.

stmnt1:

let m = 4 then r = 12
let m = 6 then r = 18

Hence insuff

stmnt2:
We can have different combinations for this as well

m= 10 and r = 14
m = 6 and r = 18

Hence insuff

taking together when m = 6 then r = 18 and 12 is halfway between m and r

also for m = -12 r = +36, 12 is halfway of m and r and r = 3 times the distance from 0 and m (distance is +ve value)
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rr [#permalink]  29 Jan 2012, 11:00
Algebraically this can be solved as a system of two equations

|r| = 3|m|

\frac{m+r}{2}=12

1) m=6; r=18
2) m=-12; r=36

Not sufficient, so the answer is E
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What is the value of r? [#permalink]  13 Feb 2012, 15:53
If m and r are two numbers on the number line, what is the value of r?

(1) The distance between r and 0 is three times the distance between m and 0
(2) 12 is halfway between m and r
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Re: What is the value of r? [#permalink]  13 Feb 2012, 18:10
jj97cornell wrote:
If m and r are two numbers on the number line, what is the value of r?

(1) The distance between r and 0 is three times the distance between m and 0
(2) 12 is halfway between m and r

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Re: What is the value of r?   [#permalink] 13 Feb 2012, 18:10
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