Bob goes to his class reunion at Haughty College. Fifteen other graduates show up: every one of them went on, as Bob did, to become either a doctor or a lawyer. Bob's notices the following: more than half are doctors and more than half of the doctors are women, but women lawyers outnumber women doctors in the group. He also notices that even if he is counted with the others (so there would be 16), these statements still hold true. How many women lawyers are there, and what is Bob's profession?

PLEASE HELP!

If Bob is a doctor,
Standing outside the room observing his classmates and there are 8 doctors, 5 female and 3 male, or 6 female and 2 male, and 7 lawyers all of the conditions are met. The number of doctors exceeds the number of lawyers, the number of female doctors exceeds the number of male doctors. If the number of female doctors is 5, then 6 of the lawyers must be female. If the number of female doctors is 6 then all of the lawyers (7) must be female. When Bob enters the room the number of doctors increases but is still greater than the number of lawyers. If the ratio of female doctors to male doctors was 5 to 3, it has changed to 5 to 4 but the number of female doctors still exceeds the number of male doctors. If the ratio of female to male doctors was 6 to 2 it has changed, but the number of female doctors still exceeds the number of male doctors. If the mix of female to male doctors was 5 to 3 then 6 or more of the 7 lawyers must be female for all of the conditions to be met after Bob entered the room. If the ratio of female to male doctors was 6 to 2 then all of the 7 of the lawyers must be female. So the number of female lawyers depends on the number of female doctors.

If Bob is a lawyer,
Standing outside the room observing his classmates and there are 8 doctors, 5 female and 3 male, or 6 female and 2 male, and 7 lawyers all of the conditions are met. The number of doctors exceeds the number of lawyers, the number of female doctors exceeds the number of male doctors. If the number of female doctors is 5, then 6 of the lawyers must be female. If the number of female doctors is 6 then all of the lawyers (7) must be female. As soon as Bob steps into the room the number of doctors no longer exceeds the number of lawyers, so the first condition is not met.

If Bob is a doctor,
Standing outside the room observing his classmates and there are 9 doctors, 5 female and 4 male, and 6 lawyers all of the conditions are met. There cannot be more than 5 female doctors because the number of lawyers must exceed the number of female doctors. As soon as Bob steps in the room the number of doctors in the room changes and the ratio of female to male doctors goes down. The number of female doctors no longer exceeds the number of male doctors.

If Bob is a lawyer,
Standing outside the room observing his classmates and there are 9 doctors, 5 female and 4 male, and 6 lawyers, all of the conditions are met. The number of doctors exceeds the number of lawyers, the number of female doctors exceeds the number of male doctors. If all of the lawyers are female, the number of female lawyers exceeds the number of female doctors. As soon as Bob steps into the room nothing changes except the number of people in the room. The number of doctors (9) still exceeds the number of lawyers (7). The number of female doctors (5) still exceeds the number of male doctors (4). The number of female lawyers (6) exceeds the number of female doctors (5).

So, if Bob is a lawyer and the number of female doctors in the room is 5, the number of female lawyers is 6.

If Bob is a doctor and the number of female doctors in the room is 5 then the number of female lawyers could be 6 or 7. If the number of female doctors is 6 then there must be 7 female lawyers.

No way to tell whether Bob is a doctor or a lawyer with out knowing the number of doctors in the room and the ratio of female to male.
If there are 9 doctors in the room, of which 5 are female, Bob is a lawyer.

Agreed - the problem is indeterminate as written. If there are 8 doctors in the room before Bob enters, then there are either 6 or 7 female lawyers and Bob is a doctor. If there are 9 doctors in the room before he enters, then there are 6 female lawyers and Bob is a lawyer.