Trying my hand at question crafting.
A: |x^3| + |x^2| -x
B: -x^3 + |2x^3| + |x^2| - |x|
Hint: This one really punishes a few common strategies. It will seem either impossible or way too easy, it should force you to try different approaches.
@Leaderboard you might enjoy looking at this
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Ok, spoiler, I don’t think anybody else is looking at this one.
In desmos you should see that the two are equal for -1, 0, and all positive numbers, which should mess with choosing numbers. The abs vals will complicate strict algebra. You’ll want to use conceptual understanding of exponents and manipulation to simplify the equation, noting that |x^2| is a red herring and can just be removed.
@Leaderboard I started thinking of problems like this when I was trying to force myself to bounce between different strategies mid question. This one is unforgiving if you don’t try different approaches.
It’s probably too much for a real GRE question but felt like useful practice and conceptual review.
The answer here is D.
I didn’t respond to it because I thought you weren’t expecting one, sorry.
I think your “positive numbers” case can be weeded out by simply removing the absolute values:
QA: x^3 + x^2 - x
QB: -x^3 + 2x^3 + x^2 - x
→ they are the same.
So I would then just do this when x < 0 or choosing numbers:
QA: -x^3 + x^2 - x
QB: -x^3 - 2x^3 + x^2 + x
and they are not the same. I thinking choosing numbers would still work as long as you know what’s going on.
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