One logistic regression has a 'model 7' taking into account many factors where going from 1300 to 1600 goes from an odds ratio of 1.907 to 10.381; so if I'm interpreting this right, an extra 10pts on your total SAT is worth an odds ratio of ((10.381 - 1.907) / (1600-1300)) * 10 + 1 = 1.282.

Aren't odds ratios multiplicative? It also seems to me that we should take the center of the SAT score bins to avoid an off-by-one bin width bias, so (10.381 / 1.907) ^ (10 / (1550 - 1350)) = 1.088. (Or compute additively with log-odds.)

As Vaniver mentioned, this estimate varies across the SAT score bins. If we look only at the top two SAT bins in Model 7: (10.381 / 4.062) ^ (10 / (1550 - 1450)) = 1.098.

Note that within the logistic model, they binned their SAT score data and regressed on them as dichotomous indicator variables, instead of using the raw scores and doing polynomial/nonparametric regression (I presume they did this to simplify their work because all other predictor variables are dichotomous).