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

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01 May 2011, 02:51

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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

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

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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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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)

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

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18 Sep 2015, 01:20

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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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18 Sep 2015, 11:49

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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.

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

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30 Sep 2015, 01:03

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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

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

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17 Oct 2015, 02:43

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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?

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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21 Nov 2015, 08:29

Please tag Absolute Value Thank you

jamifahad wrote:

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

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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31 Dec 2016, 09:41

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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]

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

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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"

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

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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

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

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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.

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

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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.

Attachments

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Last edited by gary391 on 24 Jul 2017, 12:18, edited 6 times in total.

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

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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

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.

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