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

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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 02 Jul 2018, 21:02
generis wrote:
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.

In addition, my post has three links that explain. Please read them.


I believe you are referring to OG18 question number 116

Note..This question is not asking AM of r,s,t.

It is asking AM of R,S,T..
Now for absolute values |X|=Y
x>0
mean
X=Y
X<0
means
X=-Y

So we get r=-R,s=S,t=T
For R<0 r=-R

Therefore clearly option e

(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 08 May 2019, 04:40
This question has some clever wording in it. The question mentions that coordinates R, S, T have absolute values r, s, t.

The question then asks for the average of R, S, T but uses r, s, t (i.e. the absolute values) in the answer choices.

Therefore, to take into account the fact that coordinate R is a negative, we must multiply r by -1. As a result, the correct answer choice becomes (s + t - r) / 3. 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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New post 14 May 2019, 02:07
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 ??



Hi longhaul123

Try to think in the easiest manner possible ignoring absolute value or any fancy stuff, I too was confused at the starting.

consider 3 integers: -7(R), 5(S),and 8(T)

If someone asks to find the mean (average) of the 3 numbers above, we can say

\(\frac{-7 + 5 + 8}{3}\) -------> st1

Now, when the question says absolute value they have simply given the positive value of each term i.e: |-7|--> 7(r), |5|--> 5(s), |8|--> 8(t)

Since, to find mean (average), as in st1 above, it is necessary to consider the sign (+/-) of the number the answer is (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 05 Aug 2019, 19:32
Here is my interpretation of this question.

Take aside the portion saying absolute values, we know basic average is simply adding all of the numbers and dividing by the number of numbers. Say R is -4, S is 1 and T is 2. We know the average would be (-4 + 1 + 2)/3.

The question itself is a very tricky/deceptive in the wording. It says the number line has the points R, S, and T with the absolute values of r, s, and t. While R, S and T might have absolute values of r, s and t, the question ultimately asks what the average of points R, S and T are, not r, s and t. The key might be in the use of the word "coordinate" which factors in positive/negative values, instead of the absolute value of r, s and t.

It wants the average to EQUAL the coordinates of R, S, and T. So all we need is an equation that equals the average of (-4 + 1 +2)/3. E (s + t - r)/3 is the only option that equals that.

Ultimately r, s, and t are absolute values, so the the average equation would have to incorporate a negative for r. So (|s| + |t| - (|r|))/3

Bunuel wrote:
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 13 Sep 2019, 22:32
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

Attachment:
2015-09-18_1954.png


Since absolute values r, s & t > 0
But real values of S & T > 0 But R < 0
Therefore real values of R, S & T are -r, s & t respectively

Average of R, S & T = (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 24 Oct 2019, 04:23
1
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

Attachment:
2015-09-18_1954.png


Responding to a pm:

Note that point R is to the left of 0 so it will be negative. S and T are to the right of 0 so they are positive.
Say R = -4, S = 2, T = 3

We are given that r, s and t are absolute values of the co-ordinates so r = 4, s = 2 and t = 3 (absolute values are positive)
So R = -r

Average of the co-ordinates of points R, S and T = (R + S + T)/3 = (-r + s + t)/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 23 Nov 2019, 14:16
VeritasKarishma, can you please explain as to why did we not consider the absolute value of R to calculate the mean? The question mentions that the points on the number line have absolute values.

Thanks!
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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 24 Nov 2019, 22:32
RJ7X0DefiningMyX wrote:
VeritasKarishma, can you please explain as to why did we not consider the absolute value of R to calculate the mean? The question mentions that the points on the number line have absolute values.

Thanks!


Small letters r, s and t are variables. The question defines them as absolute values of the points R, S and T. But the question asks for the average of the actual co-ordinates of R, S and T. It does not ask for the average of r, s and t. That would simply be (r+s+t)/3.
But the actual co-ordinate of R would be -r since it will be negative.
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Re: The number line shown contains three points R, S, and T, whose coordin   [#permalink] 24 Nov 2019, 22:32

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