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If m and r are two numbers on a number line, what is the [#permalink]
 03 Jun 2006, 23:23
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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Manager
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Edit!
Sorry, Didn't read the question right. It should be C.
Let distance between O and m be d.
m/r = d/3d
r=3m
Now from ii, r-m=12
3m-m =12
m = 6 and r=36.
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E .
first tells r= 3m or r = -3m ,distance has no sign
second tells m + r = 24
hence there are more than one solutoion.
(6, 18 ) and (-12 , 36)
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Intern
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E it is..
Excellent explanation guptaraja..
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If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut.
Albert Einstein
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Manager
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I think it should be C as distance can never be negative.
e.g say M is at -3 then the distance from O is 0-(-3) = 3
or if it M is +ve 3 then the distance is 3-0 = 3
What is the OA
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(E) by the same way that guptaraja uses
1) |r| = 3*|m|
r=3*m
or
r=-3*m
2) 12 = (r+m)/2
<=> r+m = 24
There are 2 solutions by combining (1) and (2).
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pesquadero wrote: Edit!
Sorry, Didn't read the question right. It should be C.
Let distance between O and m be d.
m/r = d/3d
r=3m
Now from ii, r-m=12
3m-m =12
m = 6 and r=36 ????.
Since distance can not be negative, r = 18.
Regards,
Brajesh
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The problem is speaking about 2 numbers r and m on a number line: so they can be poisitive or negative.
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what is the OA?
C was my answer
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Fig wrote: The problem is speaking about 2 numbers r and m on a number line: so they can be poisitive or negative.
Numbers can be +ve and -ve but not the distance.
The question says
(1) The distance between r and 0 is 3 times the distance between m and 0.
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humans, I noticed that i was not enough accurate on my second post .... after mid night reply ? 
We look for r and m which are real numbers (+ or -) not distances (only +).
(1) gives us an equation with absolute values of r and m (distance).
Thus, (E) because we stay with 2 possible solutions with (1) and (2) used together.
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Fig wrote: humans, I noticed that i was not enough accurate on my second post .... after mid night reply ? We look for r and m which are real numbers (+ or -) not distances (only +). (1) gives us an equation with absolute values of r and m (distance). Thus, (E) because we stay with 2 possible solutions with (1) and (2) used together. Sorry Fig, But I still doesn't agree with you
You are absolutely right that we are looking for real number in the question which can be positive or negative.
But with statement 1 the equation is always going to be +ve and not absolute value as it is describing the distance.
e.g say if you have to calculate distance between points O and S which are at 0 cm and -7 cm on number line you are going to say the distance from O to S is 7 cm and not -7 cm.
Furthermore when solving both the equations it gives m = 6 and r = 18 which in turns authenticate the statement which says "12 is halfway between m and r"
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humans wrote: Fig wrote: humans, I noticed that i was not enough accurate on my second post .... after mid night reply ? We look for r and m which are real numbers (+ or -) not distances (only +). (1) gives us an equation with absolute values of r and m (distance). Thus, (E) because we stay with 2 possible solutions with (1) and (2) used together. Sorry Fig, But I still doesn't agree with you You are absolutely right that we are looking for real number in the question which can be positive or negative. But with statement 1 the equation is always going to be +ve and not absolute value as it is describing the distance. e.g say if you have to calculate distance between points O and S which are at 0 cm and -7 cm on number line you are going to say the distance from O to S is 7 cm and not -7 cm.Furthermore when solving both the equations it gives m = 6 and r = 18 which in turns authenticate the statement which says "12 is halfway between m and r" In bold, this is the point .
Either S=7cm or S=-7cm, OS=SO=7=|0-S|=|S-0|.
thus, |r-0|=3*|m-0| and we cannot say r > 0 and m > 0.
What is OA?
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Great discussion and a good question.
From 1. |r| = 3*|m| -- INSUFF - many values satisfy this condition
From 2. (r+m)/2 = 12 -- Similarly INSUFF
|r| = 3*|m| means there are two possibilities
a) r = 3*m
b) -r = 3*m
Using (2) -- (r+m)/2 = 12 and (a) & (b) we get two values for r and m
(r,m) = (6,12) or (-12,36).
I would pick E too.
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- Bernard Edmonds
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Agree with E. Two solutions with combined. (6,18) and (-12, 36).
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Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
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Fig, that was simply awesome. Many Many thanks for the explanation and bearing with me 
I know you can understand what will happen if a person who always used to fail in his high school will touch it after 13 long years.
Once again thanks for the explanation.
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Humans, take it easy .... I'm the first to do mistake
Have a nice day
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