[Guest]

"The hospital staff consists of 16 doctors and nurses, including me. The following facts apply to the staff members; whetheryou include me or not does no tmake a difference. The staff consists of:

(a) More nurses than doctors.

(b) More male doctors than male nurses.

© More male nurses than female nurses.

(d) At least one female doctor."

What is the gender and occupation of the speaker?

[bonanova]

Including the speaker we have

6 male doctors

5 male nurses

4 female nurses

1 female doctor

Only one person can be excluded and obey the terms of the OP:

6 male doctors

5 male nurses

3 female nurses

1 female doctor

Speaker is a female nurse.

[Guest]

6 male doctors

5 male nurses

4 female nurses

1 female doctor

According to the speaker's profile he's male.

The profile lists no occupation, so, from the OP, he's either a doctor or a nurse.

If "including me" refers to the closest antecedent, then he's a nurse.

However, doesn't it say "whether you include me or not"? If the person is a male nurse, and he is not included, then there would be 4 male nurses counted which is not greater than 4 female nurses. It says there have to be more male nurses than female nurses , not necessarily including the speaker.

right?

[Brandonb]

"The hospital staff consists of 16 doctors and nurses, including me. The following facts apply to the staff members; whetheryou include me or not does no tmake a difference. The staff consists of:

(a) More nurses than doctors.

(b) More male doctors than male nurses.

© More male nurses than female nurses.

(d) At least one female doctor."

What is the gender and occupation of the speaker?

Female Nurse

[bonanova]

Agree with both previous posters ... my first post missed it.

[Guest]

Let's go step by step and construct the staff from scratch. Statement D says that there's at least one female doctor, so let's say FD (Female Doctor) is one for now.

MD: 0

FD: 1

MN: 0

FN: 0

Statement C says that there are more male nurses than female nurses. So even if there are no female nurses, there must be at least one male nurse. Statement B says that there are more male doctors than male nurses, and since we've just established that there must be at least one male nurse, there must be at least two male doctors.

MD: 2

FD: 1

MN: 1

FN: 0

Statement A says that there are more nurses than doctors, but right now we have one nurse and three doctors. Adding a male nurse means that we must also add a male doctor to keep statement B true, so that doesn't help. Adding a female nurse means that we must also add a male nurse to keep statement C true, and consequently we must add a male doctor to keep statement B true, which adds two nurses and one doctor, which helps us. We need to do this three times for there to be more nurses than doctors.

MD: 5

FD: 1

MN: 4

FN: 3

Now all four statements are true and we have a staff of thirteen people, which means we still need three people. So what kinds of people do we add?

Adding a female doctor means we must add a female nurse or a male nurse to keep statement A true. But adding a female nurse would mean adding a male nurse, which would mean adding a male doctor, which would put us at seventeen people. Adding a male nurse would mean adding a male doctor which would make statement A false. So we can't have another female doctor.

Adding a male doctor means we must add a female nurse or a male nurse to keep statement A true. Adding a female nurse would mean adding a male nurse, which would mean adding a male doctor (which we just did). Adding a male nurse would work, but we'd be at fifteen people and the only person we could add is a female nurse.

Adding a male nurse means we must add a male doctor to keep statement B true. But we'd be at fifteen and the only person we could add is a female nurse, leading to the same combination as the previous case.

Adding a female nurse means we must add a male nurse, which means that we must also add a male doctor, leading to the same combination as the previous two cases.

So we add a female nurse, a male nurse and a male doctor.

MD: 6

FD: 1

MN: 5

FN: 4

So now we have a staff of sixteen and we just need to find the speaker. The speaker said "whether you include me or not does not make a difference", so the four statements must remain true even if we remove the speaker. Removing a male doctor would make statement B false. Removing a female doctor would make statement D false. Removing a male nurse would make statement C false. Removing a female nurse wouldn't make any of the statements false, so the speaker must be a female nurse.

Answer: the speaker was a female nurse.

Edited May 23, 2008 by flowstoneknight

[Guest]

the speaker is a female nurse