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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] New post 03 Jun 2006, 22:23
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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 [#permalink] New post 04 Jun 2006, 11:29
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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 [#permalink] New post 04 Jun 2006, 19:20
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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 [#permalink] New post 04 Jun 2006, 22:58
E it is..
Excellent explanation guptaraja..
:-)
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 [#permalink] New post 05 Jun 2006, 00:28
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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 [#permalink] New post 05 Jun 2006, 08:49
(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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 [#permalink] New post 05 Jun 2006, 09:07
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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 [#permalink] New post 05 Jun 2006, 13:15
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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 [#permalink] New post 05 Jun 2006, 16:09
what is the OA?

C was my answer
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 [#permalink] New post 05 Jun 2006, 18:37
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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 [#permalink] New post 06 Jun 2006, 00:38
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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 [#permalink] New post 06 Jun 2006, 04:37
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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 [#permalink] New post 06 Jun 2006, 05:44
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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 [#permalink] New post 06 Jun 2006, 05:53
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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 [#permalink] New post 06 Jun 2006, 08:05
Agree with E. Two solutions with combined. (6,18) and (-12, 36).
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 [#permalink] New post 06 Jun 2006, 16:02
Fig, that was simply awesome. Many Many thanks for the explanation and bearing with me :oops:

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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 [#permalink] New post 07 Jun 2006, 00:41
Humans, take it easy :).... I'm the first to do mistake ;)

Have a nice day :)
  [#permalink] 07 Jun 2006, 00:41
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