A polytechnic runs two branches. In each branch, a larger share of the women who applied to it were admitted than of the men who applied to it. Yet of all the women who applied to the polytechnic, a smaller share were admitted than of all the men who applied. Which of the following, if true, best accounts for both findings together?

The two findings sit together as soon as the two groups are not spread alike over the two branches. Put the women almost entirely into the hard branch and the men almost entirely into the easy one, and the women can be treated better than the men wherever they are judged while still finishing with the poorer overall share, because most of them were judged where almost nobody gets in. The manner of admission does not touch how the applicants were distributed. More men applying in all changes the size of the groups without changing either share. And better marks among the women makes the two findings harder to reconcile rather than easier.