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The number line shown contains three points R, S, and T, whose coordin

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The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s, and t, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points R, S, and T ?

A. s
B. s + t - r
C. (r - s - t)/3
D. (r + s + t)/3
E. (s + t - r)/3

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[Reveal] Spoiler: OA

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Last edited by Bunuel on 18 Sep 2015, 08:55, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 01 May 2011, 03:18
As R is to the right of the origin,essentially it has negative value.
therefore arithmetic mean = (s+t-r)/3 will be the right expression as S and T are positive numbers.
Hence E.
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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 01 May 2011, 04:34
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The arithmetic mean of three numbers x y z is (x+y+z)/3

In this case we know that the numbers are s, t, -r (since r is the absolute value of a negative number ... and s,t are the absolute values of positive numbers)

Hence mean is (s+t-r)/3

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 01 May 2011, 04:51
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shrouded1 wrote:
In this case we know that the numbers are s, t, -r (since r is the absolute value of a negative number


\(|r| = r when r > 0\)
\(= -r when r < 0\)
and since r < 0, it should be -r
Am i correct?
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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 01 May 2011, 06:38
Spot on

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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I don't really get the logic here. The absolute value of any number is > 0.
r is a negative number on the line I-r I = r. The only explanation for this solution I see is that, the absolute value of -r is >0, but the value of r is negative (within the absolute brackets), and in the calculation of average we are using r and not an absolute value of r please correct if I'm wrong.
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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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BrainLab wrote:
I don't really get the logic here. The absolute value of any number is > 0.
r is a negative number on the line I-r I = r. The only explanation for this solution I see is that, the absolute value of -r is >0, but the value of r is negative (within the absolute brackets), and in the calculation of average we are using r and not an absolute value of r please correct if I'm wrong.


I was wondering the same thing. I marked D as answer taking absolute values.
Need some explanation here.

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 20 Sep 2015, 01:22
Hi Bunuel ,

would please explain the concept for absolute number and details explain solution of this question .

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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I am wondering the same thing ...otherwise why would the question mention absolute values if you want us to take the sign of the number into consideration. Absolute values meaning all are positive. And it asks what is the average of the co-ordinates and the co-ordinates are given to be absolute values.

Would be grateful if someone can shed some light on this. Thnx

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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Hi, I would also like to clarify this solution. If r is the absolute value of R and R is -R then why is the co-ordinate -r? If it is an absolute value it cannot be a negative number. Please explain?

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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mrai87 wrote:
Image

The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s, and t, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points R, S, and T ?

A. s
B. s + t - r
C. (r - s - t)/3
D. (r + s + t)/3
E. (s + t - r)/3

Hi, I would also like to clarify this solution. If r is the absolute value of R and R is -R then why is the co-ordinate -r? If it is an absolute value it cannot be a negative number. Please explain?


Say R = -3, S = 1 and T = 2. In this case r = |-3| = 3, s = 1, and t = 2. The average of the coordinates of the points R, S, and T would be (2 + 1 + (-3))/3 so, (s + t - r)/3.
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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 16 Nov 2015, 17:55
thank you Bunuel

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 21 Nov 2015, 08:29
Please tag Absolute Value
Thank you
jamifahad wrote:
Image

The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s, and t, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points R, S, and T ?

A. s
B. s + t - r
C. (r - s - t)/3
D. (r + s + t)/3
E. (s + t - r)/3

[Reveal] Spoiler:
Attachment:
2015-09-18_1954.png

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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The number line shown contains three points R, S, and T, whose coordin [#permalink]

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I didn't find the answers above very helpful and they were all confusing. Hopefully this one is less so.

Here is an answer which to me makes more sense. We are shown a number line. An absolute value can never be negative on a number line unless the negative is outside the brackets. Therefore if R is shown as -3 on the number line it would be shown as -[-3] and if R is +3 then it would be shown as -[3]. In either case the negative outside the bracket will move it into the negative position on the number line. Therefore all the Math is S + T - +R which is (S+T-R)/ 3. So the absolute value of R is positive but because it's shown on a number line it has to have a negative infront of it. Had the Question simply asked the absolute Value of [3] +[2] +[-2] the answer would be (3+2-2) /3 but since it showed us the numbers on the number line we can conclude the number are something like [3] + [2] + -[2]

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 31 Mar 2017, 04:55
SamBoyle wrote:
I didn't find the answers above very helpful and they were all confusing. Hopefully this one is less so.

Here is an answer which to me makes more sense. We are shown a number line. An absolute value can never be negative on a number line unless the negative is outside the brackets. Therefore if R is shown as -3 on the number line it would be shown as -[-3] and if R is +3 then it would be shown as -[3]. In either case the negative outside the bracket will move it into the negative position on the number line. Therefore all the Math is S + T - +R which is (S+T-R)/ 3. So the absolute value of R is positive but because it's shown on a number line it has to have a negative infront of it. Had the Question simply asked the absolute Value of [3] +[2] +[-2] the answer would be (3+2-2) /3 but since it showed us the numbers on the number line we can conclude the number are something like [3] + [2] + -[2]


Hi Sam,

The question is asking for you to find the average of "r, s and t" that matches the average of "R, S and T."

(i) If RST = [-4, 1, 2], the average equals (-4+1+2)/3 = -1/3;
(ii) Then, |rst| = [4, 1, 2] and the only answer matching the average of RST is "(E) s+t-r/3" = (1+2-4)/3 = -1/3"

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 26 Apr 2017, 09:43
I am still confused about this absolute value still being negative in the end. If the question had been exactly the same but without mentionning absolute values:
Quote:
whose coordinates have values r, s, and t

instead of
Quote:
whose coordinates have absolute values r, s, and t

Would the result be the same ?

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Re: The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 23 May 2017, 11:06
This question is kind of Deceptive . you can still have (+(-R)+S+T)/3 to make D correct . E could also be rationalized like (S+T-(+R))/3 . This is why I hate the GMAT . We are arguing semantics/Syntax . Unless I am just dumb and don't comprehend.

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The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 23 Jul 2017, 17:49
According to the question - "coordinates have absolute values r, s, and t" -> which implies the distance of R, S & T from the origin "zero" is given i.e. the magnitude.

Since |x| = -(x) for x < 0 and |x| = (x) for x>=0.

example:

consider R = -4, S=2, t=3 based on the question

we are given, absolute value of R --> r = -(-4) = 4
we are given, absolute value of S --> s = (2) = 3
we are given, absolute value of T --> t = (3) = 3


Now, the question is asking for a mean of all these coordinates. Since the points are distributed across origin 0. In order to calculate the mean we will have to add the coordinates then divide by the number of coordinates. As the coordinate R is on the -ve side of origin we will have to use a -ve sign i.e. -r

Thus, the answer will be (s+t-r)/3

Note: Assuming if we are not given the absolute value information we can calculate the mean of the coordinates based on the placement of the coordinates on the number line, the only caveat being that the coordinates should be clearly mentioned w.r.t to the origin on the number line.
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The number line shown contains three points R, S, and T, whose coordin [#permalink]

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New post 24 Jul 2017, 07:16
NanaA wrote:
This question is kind of Deceptive . you can still have (+(-R)+S+T)/3 to make D correct . E could also be rationalized like (S+T-(+R))/3 . This is why I hate the GMAT . We are arguing semantics/Syntax . Unless I am just dumb and don't comprehend.

You certainly are not dumb; your intelligence led you to see that the way absolute value is often taught, and the way it shows up here, seem incongruent.

I'll avoid the semantics / syntax categorization, except to say that, overly simplified, the issue is what "absolute value" denotes.

In this case, we have a negative variable, -r. It might help to memorize this rule: If r is negative, i.e. if r < 0, then |r| = -r.

NOVA explains the latter equality's seeming contradiction. "This often confuses students because the absolute value is positive, but the -r appears to be negative." The latter isn't negative.

"It is actually positive -- it is the negative of a negative number, which is positive."

The authors also write, "Another way to view this [seeming contradiction] is

|x| = -x = (-1)(a negative number) = a positive number."

For the quoted material as well as the full explanation from NOVA, see these two sites (the second is more thorough):

Nova Press,GMAT Math Strategies, "Absolute Value," (scroll down a long way)
http://novapress.net/gmat/gmat-strategies/gmat-math-strategies/ (accessed 7/24/17), and

"Absolute Value,"
https://gradestack.com/GRE-Complete-Tutor/Inequalities/Absolute-Value/16611-3354-13054-study-wtw (accessed 7/24/17)

I had to teach myself Algebra 1 and 2. In the U.S., my textbooks were (and may still be) unhelpful at best with this issue. My eyes were crossed. Sometimes they still are. I understand, but not always.

So I memorized the rule and the method for solving, and left it at that.

For this problem, I assigned values to the variables and calculated the mean with numbers that had both the intuitively correct signs, and, given the rule, the mathematically correct signs. (-1 + 2 + 5)/3 = mean of 2.

Here is another link to a great post that might help, Bunuel, Absolute Value, Tips and Tricks,
https://gmatclub.com/forum/absolute-value-tips-and-hints-175002.html

Hope this helps.:-)

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