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Senior Manager  Joined: 03 Mar 2010
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Schools: Simon '16 (M$) The number line shown contains three points R, S, and T, whose coordin [#permalink] ### Show Tags 9 1 83 00:00 Difficulty:   15% (low) Question Stats: 71% (00:54) correct 29% (00:58) wrong based on 2421 sessions ### HideShow timer Statistics The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s, and t, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points R, S, and T ? A. s B. s + t - r C. (r - s - t)/3 D. (r + s + t)/3 E. (s + t - r)/3 Attachment: 2015-09-18_1954.png [ 5.82 KiB | Viewed 37645 times ] _________________ My dad once said to me: Son, nothing succeeds like success. Originally posted by jamifahad on 01 May 2011, 01:51. Last edited by Bunuel on 18 Sep 2015, 07:55, edited 1 time in total. Renamed the topic, edited the question and added the OA. ##### Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 62498 Re: The number line shown contains three points R, S, and T, whose coordin [#permalink] ### Show Tags 12 7 mrai87 wrote: The number line shown contains three points R, S, and T, whose coordinates have absolute values r, s, and t, respectively. Which of the following equals the average (arithmetic mean) of the coordinates of the points R, S, and T ? A. s B. s + t - r C. (r - s - t)/3 D. (r + s + t)/3 E. (s + t - r)/3 Hi, I would also like to clarify this solution. If r is the absolute value of R and R is -R then why is the co-ordinate -r? If it is an absolute value it cannot be a negative number. Please explain? Say R = -3, S = 1 and T = 2. In this case r = |-3| = 3, s = 1, and t = 2. The average of the coordinates of the points R, S, and T would be (2 + 1 + (-3))/3 so, (s + t - r)/3. _________________ ##### Most Helpful Community Reply Current Student B Joined: 10 Mar 2013 Posts: 452 Location: Germany Concentration: Finance, Entrepreneurship Schools: WHU MBA"20 (A$)
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Re: The number line shown contains three points R, S, and T, whose coordin  [#permalink]

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8
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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1
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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3
3
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

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

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2
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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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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1
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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2
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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The number line shown contains three points R, S, and T, whose coordin  [#permalink]

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3
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 -. 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  + +[-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  +  + -
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Re: The number line shown contains three points R, S, and T, whose coordin  [#permalink]

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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 -. 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  + +[-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  +  + -

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"

Rgds
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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 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

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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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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1
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 absolute_value.JPG [ 16.74 KiB | Viewed 25528 times ]

Originally posted by gary391 on 23 Jul 2017, 16:49.
Last edited by gary391 on 24 Jul 2017, 11:18, edited 6 times in total.
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The number line shown contains three points R, S, and T, whose coordin  [#permalink]

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3
2
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 $$|r| = -r$$

The expression on the RHS ($$-r$$) is not negative. It is positive. It is the negative (opposite) of a negative value:

$$-(-5) = 5$$

Another way to see it; if x is a negative number

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

|-3| =
-(-3) =
(-1)(the negative number -3) =
3

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.
Only Answer E gives that result.

A great post that might help: Bunuel ,Absolute Value, Tips and Tricks,here.

These sites might also help.
Scroll a long way for a discussion of absolute value and negative numbers, here,

and here.

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

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5 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

We can let R, S, and T be the actual values. Thus, we want to determine the value of (R + S + T)/3. Since S and T are positive, S = s and T = t. However, since R is negative, R = -r. Thus, the average becomes:

(-r + s + t)/3

(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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Here in this question if the question would ask the average of r,s,t then the average would be r+s+t/3 because r is the absolute value?? 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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If I take R=l-3l and s=1, R=2, the average is (3+2+1)/3= 2 as r (coordinates have absolute values r, s, and t,) and from D I can find the required answer which is D. I am wrong but don't know why. Could you please explain how this portion "whose coordinates have absolute values r, s, and t, respectively." is affecting the question and what does it mean? Thanks Bunuel VeritasPrepKarishma chetan2u
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Re: The number line shown contains three points R, S, and T, whose coordin  [#permalink]

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can someone help me with this question. We are asked to calculate the average of the co-ordinates of the points R , S and T and that they are all positive since we are given that the absolute values of the co ordinates are given . Then how is it possible to consider the negative value of R ??
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The number line shown contains three points R, S, and T, whose coordin  [#permalink]

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longhaul123 wrote:
can someone help me with this question. We are asked to calculate the average of the co-ordinates of the points R , S and T and that they are all positive since we are given that the absolute values of the co ordinates are given . Then how is it possible to consider the negative value of R ??

longhaul123 , posts above explain.

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