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.

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 donâ€™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. Youâ€™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 donâ€™t try different approaches.

Itâ€™s probably too much for a real GRE question but felt like useful practice and conceptual review.

The answer here is D.

I didnâ€™t respond to it because I thought you werenâ€™t expecting one, sorry.

I think your â€śpositive numbersâ€ť 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

â†’ 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 whatâ€™s going on.

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