Good question - it's not uncommon for Data Sufficiency statements to be a little bit abstract, so strategically when that happens you often want to try plugging in numbers with different properties to see whether they satisfy the statement. That way you can get a better feel for what the statement really says. Here, you could try:
If m = 5, does the relationship hold?
abs val (5) = 5 ---> Yes
If m = -4, does the relationship hold?
abs val (-4) = 4, which does not equal our value of m (-4) ---> No
So it appears that the relationship does not hold for negative numbers, but it does for positive numbers. What about fractions?
abs val (2/3) = 2/3 ---> Yes for a positive fraction
abs val (-3/4) = 3/4, which doesn't equal our m (-3/40), ----> No for a negative fraction
What about 0, which often has its own properties?
abs val (0) = 0 ---> Yes for 0
So it looks like the relationship holds for positive numbers and for 0, but not for negative numbers. (And that is the rule - the absolute value of a number signifies its distance from 0 on a number line, so the range for absolute values is anything > or = 0)
Now, that's probably a property you should just know cold heading into the test. But if you're ever unsure of what a statement is telling you, you can better assess it by trying numbers with different properties so that you can get a feel for what that relationship means.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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