Properties of Absolute Value

[rihanna.hayat]

Hi friends,

Just wanted to share some properties of Absolute Value. This is not for memorization.
Please check if I am providing correct info and please share some advance properties of Absolute Value which may be helpful in GMAT CAT.

For all real values of a and b:

1. lal + lbl > la+bl
2. lal + lbl > la-bl
3. lal + lbl > lal - lbl
4. lal + lbl > llal - lbll
5. lal - lbl < la-bl < lal + lbl
6. la+bl > la-bl ; if ab>0
7. la+bl < la-bl ; if ab<0
8. la-bl^2 = (a-b)^2 = a^2 + b^2 -2ab
9. [lal - lbl]^2 = a^2 + b^2 -2 lal.lbl

[RonPurewal]

These all look correct.

More importantly, though, there's really no point in learning "properties" like these for the GMAT. If any of these inequalities were to surface in a GMAT problem, one could simply plug in the different combinations of signs to test them out.

In fact, learning these kinds of things is probably more likely to be counterproductive than to be productive. If someone walked into the GMAT with twenty or thirty "rules" like this in his or her head, then that person would be much more likely to miss easy patterns or to overcomplicate simple problems.

[rihanna.hayat]

More importantly, though, there's really no point in learning "properties" like these for the GMAT. If any of these inequalities were to surface in a GMAT problem, one could simply plug in the different combinations of signs to test them out.

Thanks Ron.
Just wanted to know the best(less time consuming) way to solve problems involving absolute value.
Got this problem in GMAT Prep
Is lx-yl>lxl - lyl
(1) y<x
(2) xy<0

Although I solved the problem by substituting different numbers with different signs for X and Y but it took more than 4 mins trying combinations such as:(values in order x......y)
For condition (2)
-2.......3 (x<y)
-3.......2 (x<y)
2........3 (x<y)
3........2 (x>y)
2.......-3 (x>y)
-2......-3 (x>y)

Also at the end it was really confusing.

Please guide.
Thanks.

[RonPurewal]

well, i can see what the problem is: you are still unclear on the fundamentals of how data sufficiency works.

when you are working with one of the statements, that statement must be TRUE!
in other words, you don't need to consider any cases that violate the statement.

look at how you dealt with statement 2:

it took more than 4 mins trying combinations such as:(values in order x......y)
For condition (2)
-2.......3 (x<y)
-3.......2 (x<y)
2........3 (x<y)
3........2 (x>y)
2.......-3 (x>y)
-2......-3 (x>y)

the 3 red pairs aren't even relevant here, because those don't satisfy statement 2 (xy < 0) in the first place. why would you plug in values that don't satisfy the initial requirement?

try re-visiting our basic DS materials and acquiring a more solid (and more rapid) understanding of how data sufficiency works in the first place.
until you acquire that understanding -- i.e., until you get to the point where you immediately understand what you are actually supposed to do here -- there's little point in thinking about things that are "less time-consuming".

[rihanna.hayat]

Hi Ron,

Actually by mistake I wrote that the options are only for condition 2. I gave a list combining options for both the conditions, although after your comment I realized that option (x=2....y=3) does not fit under any condition.
the last three options I tried for condition (i) y<x, but (x=2...y=-3) for condition (ii) as well.

Thanks for pointing out.

[jlucero]

Hi Ron,

Actually by mistake I wrote that the options are only for condition 2. I gave a list combining options for both the conditions, although after your comment I realized that option (x=2....y=3) does not fit under any condition.
the last three options I tried for condition (i) y<x, but (x=2...y=-3) for condition (ii) as well.

Thanks for pointing out.

As long as you are understanding those concepts, that's what's most important here. And it's good to be thorough here, but on the real test, you want to be looking for one "no" and one "yes" answer. NOT trying to test out every possible situation (although sometimes you will have to if everything is turning up "no" or "yes".