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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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56% (00:46) wrong based on 44 sessions
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.
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Re: Number Line - DS [#permalink]
18 Dec 2009, 17:49
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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=18OR r=-3m --> r+m=-3m+m=24 --> m=-12 and r=36Two different values for r. Not sufficient. Answer: E.
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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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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]
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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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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
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Re: What is the value of r?
[#permalink]
13 Feb 2012, 18:10
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