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If m and r are two numbers on a number line, what is the [#permalink]
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03 Jun 2006, 23:23
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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.



Manager
Joined: 29 Apr 2006
Posts: 85

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, rm=12
3mm =12
m = 6 and r=36.



Intern
Joined: 05 Apr 2006
Posts: 34

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)



Intern
Joined: 04 May 2006
Posts: 49

E it is..
Excellent explanation guptaraja..
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Manager
Joined: 12 Apr 2006
Posts: 215
Location: India

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 30 = 3
What is the OA



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Joined: 01 May 2006
Posts: 1796

(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).



Director
Joined: 17 Sep 2005
Posts: 903

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, rm=12 3mm =12 m = 6 and r=36 ????.
Since distance can not be negative, r = 18.
Regards,
Brajesh



SVP
Joined: 01 May 2006
Posts: 1796

The problem is speaking about 2 numbers r and m on a number line: so they can be poisitive or negative.



Manager
Joined: 19 Apr 2006
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what is the OA?
C was my answer



Manager
Joined: 12 Apr 2006
Posts: 215
Location: India

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.



SVP
Joined: 01 May 2006
Posts: 1796

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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Joined: 12 Apr 2006
Posts: 215
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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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Joined: 01 May 2006
Posts: 1796

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=0S=S0.
thus, r0=3*m0 and we cannot say r > 0 and m > 0.
What is OA?



VP
Joined: 21 Sep 2003
Posts: 1057
Location: USA

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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SVP
Joined: 03 Jan 2005
Posts: 2233

Agree with E. Two solutions with combined. (6,18) and (12, 36).
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Manager
Joined: 12 Apr 2006
Posts: 215
Location: India

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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Joined: 01 May 2006
Posts: 1796

Humans, take it easy .... I'm the first to do mistake
Have a nice day










