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Absolute Value

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Svedankae » Thu Jun 04, 2009 2:38 am
doclkk wrote:
mike22629 wrote: But again, right now - i'm way more confused and it seems that another northern california person is too.
Hah sorry buddy, in case you were referring to me, i hate to say that im not from northern cal... but you were at least right about the confused part.



Is there nobody here who can explain what this problem is really asking?
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by mike22629 » Thu Jun 04, 2009 4:25 am
Okay, I will try one more time, and if it does not work, just ask Ian. Absolute value DOES measure distance

So for example

l5l = distance from 5 to 0
l-5l = distance from -5 to 0

BUT
when TWO terms are inside of an absolute value sign, they must be subtracted from one another to find the distance between them.

SO

lx+yl = 6, that is NOT the distance inbetween x and y because they are being added. This is the distance of x from 0 PLUS the distance of y from 0.

Look at it visually

Say x = 4, y =2

----------------------0---------y-----------------

----------------------0--------------------------------x---

So the total distance is both of these lines added together

----------------------0-----------------------------------------------(x+y)

But the distance between x and y is 2, therefore lx+yl does not equal distance between x and y, it equals the distance between x and NEGATIVE y
NOW
If you flip either y or x as negative..

--------y-------------0------------------------------------x

You can see that the distance between x and y is actually equal to lx+yl because even though they are not at the same points, the distance is the same.
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by doclkk » Thu Jun 04, 2009 4:53 am
mike22629 wrote:Okay, I will try one more time, and if it does not work, just ask Ian. Absolute value DOES measure distance

So for example

l5l = distance from 5 to 0
l-5l = distance from -5 to 0

BUT
when TWO terms are inside of an absolute value sign, they must be subtracted from one another to find the distance between them.

SO

lx+yl = 6, that is NOT the distance inbetween x and y because they are being added. This is the distance of x from 0 PLUS the distance of y from 0.

Look at it visually

Say x = 4, y =2

----------------------0---------y-----------------

----------------------0--------------------------------x---

So the total distance is both of these lines added together

----------------------0-----------------------------------------------(x+y)

But the distance between x and y is 2, therefore lx+yl does not equal distance between x and y, it equals the distance between x and NEGATIVE y
NOW
If you flip either y or x as negative..

--------y-------------0------------------------------------x

You can see that the distance between x and y is actually equal to lx+yl because even though they are not at the same points, the distance is the same.
I got it now

So distance of X from 0 and Distance of Y from 0. Sum the distances.

Got it. Very clear explanation. =)

Sorry about the trouble, I went to public school. =)
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by Svedankae » Thu Jun 04, 2009 12:29 pm
mike22629 wrote:Okay, I will try one more time, and if it does not work, just ask Ian. Absolute value DOES measure distance

So for example

l5l = distance from 5 to 0
l-5l = distance from -5 to 0

BUT
when TWO terms are inside of an absolute value sign, they must be subtracted from one another to find the distance between them.

SO

lx+yl = 6, that is NOT the distance inbetween x and y because they are being added. This is the distance of x from 0 PLUS the distance of y from 0.

Look at it visually

Say x = 4, y =2

----------------------0---------y-----------------

----------------------0--------------------------------x---

So the total distance is both of these lines added together

----------------------0-----------------------------------------------(x+y)

But the distance between x and y is 2, therefore lx+yl does not equal distance between x and y, it equals the distance between x and NEGATIVE y
NOW
If you flip either y or x as negative..

--------y-------------0------------------------------------x

You can see that the distance between x and y is actually equal to lx+yl because even though they are not at the same points, the distance is the same.
I want to thank you and everyone else who has answered in this thread. unfortunately after reading it over and over again, i still havent quite figured it out. i always thought of me as having a very solid math background (i come from germany and we kinda take math seriuosly ;)) and i also understand the idea of absolute value, but somehow this question is just not clicking. i think the main problem is that i dont really see the sense in this question

i would be extremely grateful if someone would add me on skype and maybe explain it to me via a phone call.. my nick is mostawesomect

thanks!
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by lunarpower » Fri Jun 05, 2009 2:06 am
i'll try to make this simpler.

the ABSOLUTE VALUE OF A DIFFERENCE represents distance.
absolute values of other things don't.

therefore, if you can express the absolute value as | THIS - THAT |, where THIS and THAT are two quantities, then it's a distance between THIS and THAT.

here you go:

|x + y|
this does NOT have the above form, so, right now, it doesn't represent a distance at all.

BUT
you can rewrite it in any of the following three forms:
|x - (-y)| --> therefore it's the distance between x and (-y)
|y - (-x)| --> therefore it's the distance between y and (-x)
|(x+y) - 0| --> therefore it's the distance between (x+y) and 0

(nb: none of these 3 rewrites has anything to do with absolute value craziness; all three of x - (-y), y - (-x), and (x+y) - 0 can readily be seen to be equal to x + y. instead, the issue is "how do i write x + y as a DIFFERENCE?" because only DIFFERENCES, not sums, represent distances in this context.)

it has nothing to do with the distance between x and y, since you can't express it with |x - y|.
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by Sprite_TM » Mon Jun 08, 2009 11:57 am
i am confuse too!!

why can't you just do this x + |y| = 6.

since Y is negative, you just put absolute value on Y.

and are you saying this is a fact?

|x| + |y| = |x + y| but i always thought when you put absolute values, it is like this

|x +y| = -x-y or x + y but Y is negative, so it doesnt make sense
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