How do you evaluate absolute value statements such as these?

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ogbeni: Master | Next Rank: 500 Posts; Posts: 186; Joined: Sat Sep 02, 2006 7:50 pm; Thanked: 10 times; Followed by:1 members

How do you evaluate absolute value statements such as these?

by ogbeni » Sun Sep 20, 2009 11:47 am

1. -M=|-M|

2. |P|=-|Q|

I wrote these down in my notes from some questions I took and I'm now reviewing my notes but seem to have hit a brick wall.

Also, what is the difference between the 2 statements. Per my notes, 1 could be negative or zero. I understand why it would be zero but I don't understand why it could be negative. Statement 2 is unequivocally zero but why not 1?

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Source: Beat The GMAT — Data Sufficiency | Sun Sep 20, 2009 11:47 am

m&m: Master | Next Rank: 500 Posts; Posts: 134; Joined: Sun Feb 15, 2009 7:44 pm; Thanked: 14 times

by m&m » Mon Sep 21, 2009 11:40 am

absolute signs make any sign inside (+ or -) positive (+).

So in your first example

-M=|-M|

we can simplify |-M| to |M|, so:

-M=|M|

any value of M<=0 works:

-(-1) = |-1|
1 = 1

your second example must be 0:
|P|=-|Q|

1 or -1 will not work because the absolute signs turn anything to a positive

|whatever| = +ve whatever so

+ve = -1*+ve

only 0 will make this equation work

Hope this helps