At a certain university, there are s students, \(w\) of whom are female and m of whom are male. The number of female phy

It's just a weighted average or mixtures situation. We know 12% of one group (women) and 25% of another group (men) are in physics. So overall, when we look at men and women together, somewhere between 12% and 25% are in physics. So the number of physics students p is somewhere between 12% of all students (which is 0.12s) and 25% of all students (which is 0.25s), and E is the correct answer.

The other answers can all be false. Answer A is false if we have far more female students than male students overall. Answer B is false if only a tiny fraction of the student population is female. Answer C can clearly be false, just ignoring the middle of the inequality, because w > m can be true. Answer D will only be true in the one case where men make up exactly half of the entire student body.