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

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"

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.

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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