You need to apply the marginal tax rate for California workers, which would typically be ~41% (24% federal + 9.3% state + 7.65% Social Security + Medicare), to figure out how much more is needed on a pre-tax basis. You need an extra $2.5k/month ($30k/year) pre-tax to make up a $1.5k/month difference in rent, or $3.4k/month ($40k/year) pre-tax to make up a $2k/month difference in rent, which is more realistic if you want your own apartment.
And that's just looking at the difference in rent. The number goes up further if you account for the fact that everything else is also more expensive in the Bay Area, and if you add in the additional money you need to save for a down payment, assuming you want to buy at some point. I wouldn't be surprised if that $40k/year difference ends up in the $60k-$70k range if you factor those in.
I don't doubt that a $60k-$70k difference in total comp is achievable at FANG. At startups, you probably don't get there without counting equity, which is riskier and far less liquid than equity comp at FANG.
