Jim is able to sell a hand-carved statue for $670 which was

I'm happy to help with this.

First, I'll point out, we really need a calculator for this question, so in that sense, it's not realistic as a GMAT PS problem. The GMAT is always good about giving PS problems in which there is some elegant non-calculator approach.

A tricky thing about this problem is ---- we can't simply figure out 35% of this final amount $670. In other words, going down 35% from $670 will not bring us back to the same starting point X, even though increasing 35% from X brings us to $670.

This is, in many ways, one of the most fundamental math misconceptions, and the GMAT absolutely loves to exploit it. Increasing by any percent P, and decreasing by the same percent, NEVER bring you back to the same place. For more on this, see this blog:
https://magoosh.com/gmat/2012/understand ... -the-gmat/

That blog also discusses using multipliers for percent increases & decreases, which is by far the most elegant way to handle them. Here, we start with some X that we would like to find. We increase this X by 35%. As a decimal, that's 0.35, and we add 1 to this decimal to create the multiplier for a 35% increase. This multiplier is 1.35. We know 35% more than X is $670. In other words:

670 = 1.35*X

X = 670/1.35 = 496.2962962963...

which rounds to $496.30, which is (A).

Does all this make sense?

Mike