In my physics classes, we were usually only assigned the problems with the answer in the back. We were graded on solving the problem, not providing the answer. Being able to check your numerical result against a known-good one was invaluable.
There is another side to this. In upper level mathematics courses providing answers to all (or even most) of the questions actually does a disservice to the students. It teaches the important skill of deciding if you got the answer right which is probably more useful in research/the real world.
ducd, that's the point. By only giving you half the answers, they provide enough material to learn from and test yourself against. Instructor's manual has all of the answers, so its up to the teacher to provide them.
This is fine for university students, but for anyone else, it is deeply frustrating. I don't want to have to email the author of a book merely to obtain solutions to the exercises; after all, the author may have died since they wrote the book.
The ones with the solutions in the back are for studying for the exam.
(I do find it annoying when I buy textbooks for my personal use that I don't get the answers for all the questions though. Lazy authors!)