Mission2012 wrote:Hi Mike,
Thanks for your reply. I meant absolute value (modulus). Could you please suggest how I can work on this weakness.
Regards,
Dear Mission2012,
You are not likely to see many problems such as this on the real test. The OG has almost nothing on this topic. For more information, see this blog:
https://magoosh.com/gmat/2012/gmat-math- ... te-values/
Suppose we have an equation in absolute values, and there's an inequality.
|equation| > 3
Then, this means the acceptable values could be
equation > +3 or
equation < -3
Instead, if the original inequality were:
|equation| < 3
Then, this means the acceptable values would be
-3 < equation < +3
Either way, to find this, we always solve for the equations:
equation = +3 and
equation = -3.
The solutions to those two equations will divide the number line into subsets or segments, and then you must test each segment individually, if you can't figure out by logic which segments work or don't work in the original inequality.
That's how we would solve if we had a full-blown equation, say a quadratic, in an absolute value inequality. A problem such as that, though, would be in at the very upper limit of the difficult questions the GMAT Quant will give you --- you would have to be acing everything else to get a question such as that.
More often than not, for example in OG PS #143, when the GMAT is asking about absolute value inequalities, it is not asking you to do a lot of algebra --- instead, it is testing your intuitive understanding of the
distance definition of the absolute value. I discuss this in a little more depth in the link above, but here's an overview.
Fundamentally, subtraction is about distance on the number line. That's a big idea in and of itself.
|x| = the distance x is from zero
|x - 5| = the distance x is from the point +5 on the number line
|x + 3| = the distance x is from the point -3 on the number line
Thus the absolute value inequality
|x - 7| < 2
is not something that needs any algebra to solve. Just think about the logic. We are looking for numbers, points on the number line, that are a distance of less than two from the number +7. Therefore, the points that satisfy this must be in the region
7 - 2 < x < 7 + 2
5 < x < 9
More often than not, with absolute values, as with many other operations in math, the GMAT is not trying to get you to do a ton of calculations. Rather, it is almost always looking for something quite elegant, something you solve primarily with logical insight rather than with brute force calculations. See:
https://magoosh.com/gmat/2013/how-to-do- ... th-faster/
Does all this make sense?
Mike
