Is the sentence correct or does it contain a gender neutrality problem? (Assume formal writing.) Read the article Gender-neutral writing: The pronoun problem to help you out.

1. Earl and Jeffrey decided to rent tuxes, since each wanted to look his best for the prom.a) is correctb) has a problem
2. Every first-year student entering the polytechnic university must write the mathematics aptitude test before choosing his science courses.a) is correctb) has a problem
3. If you are thinking of hiring a teenager to babysit, we recommend that you check whether she has completed our babysitter training course.a) is correctb) has a problem
4. All first-year students entering the polytechnic university must write the mathematics aptitude test before choosing their science courses.a) is correctb) has a problem
5. To save on rental fees, the company is asking everyone to bring their own lawn chair and wineglass to the staff picnic.a) is correctb) has a problem
6. Settling into her chair, the storyteller began to recount the horrifying tale of the 1917 Halifax explosion.a) is correctb) has a problem