How frequent or how many absolute value questions can we approximately expect on the GMAT? I understand there may not be a sure way to know or guess but just looking for an estimate based on past and present experiences.

Not more than a couple. The problem is that often GMAT likes to combine topics. So, you might have a geometry question which will make you use some basic absolute value concept such as area bounded by the graph of |x| + |y| = 4. So a basic understanding of all topics is a good idea even if you plan to ignore some topics.
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In the following example of 3-steps approach for complex problems


Example #1
Q.: |x+3|−|4−x|=|8+x||x+3|−|4−x|=|8+x|. How many solutions does the equation have?
Solution: There are 3 key points here: -8, -3, 4. So we have 4 conditions:

a) x<−8x<−8. −(x+3)−(4−x)=−(8+x)−(x+3)−(4−x)=−(8+x) --> x=−1x=−1. We reject the solution because our condition is not satisfied (-1 is not less than -8) Can any one please explain me how x<-8 because whenever I am doing it I am getting x>=-8 for both |8+x| and -|8+x|

b) −8≤x<−3−8≤x<−3. −(x+3)−(4−x)=(8+x)−(x+3)−(4−x)=(8+x) --> x=−15x=−15. We reject the solution because our condition is not satisfied (-15 is not within (-8,-3) interval.)

c) −3≤x<4−3≤x<4. (x+3)−(4−x)=(8+x)(x+3)−(4−x)=(8+x) --> x=9x=9. We reject the solution because our condition is not satisfied (-15 is not within (-3,4) interval.)

d) x≥4x≥4. (x+3)+(4−x)=(8+x)(x+3)+(4−x)=(8+x) --> x=−1x=−1. We reject the solution because our condition is not satisfied (-1 is not more than 4)

chetan2u Hi, sorry I keep bugging you but your explanations are easiest to understand
Can you explain to me the "trick" mentioned in the post? I don't get it :/ What are we doing after finding the mid-point?

"Problem: 1<x<9. What inequality represents this condition?

A. |x|<3
B. |x+5|<4
C. |x-1|<9
D. |-5+x|<4
E. |3+x|<5
Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let’s look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D."

This is the "trick" mentioned in the post, don't know what it means chetan2u

When are we supposed to use the 3-step method? I mean, on which kind of problems?

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Edited. Thank you.
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