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Gender and Occupation (Posted on 2012-10-22) Difficulty: 2 of 5
A member of a medical staff makes the following statements each of which is truthful:
  1. The hospital staff consists of sixteen doctors and nurses, including me.
  2. The following facts apply to the staff members; whether you include me or not does not make any difference. The staff consists of:
    • More nurses than doctors.
    • More male doctors than male nurses.
    • More male nurses than female nurses.
    • At least one female doctor.
What is the gender and occupation of the speaker?

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution solution | Comment 5 of 6 |

As there are more nurses than doctors, there must be at least nine nurses and at most seven doctors.
As there is least one female doctor, there is at most six male doctors.
As there is more male doctors than male nurses, there is at most five male nurses.
As there are more male nurses than female nurses, there is at least and at most four female nurses.
Thus, there are five male nurses, four female nurses, six male doctors, and one female doctor.

Six of the doctors are male, excluding one would make the statement that there are more male doctors than male nurses. As there is only one female doctor, her exclusion would make the statement that the staff consists of at least one female doctor false.
The exclusion of a male nurse would bring the total of male nurses equal to female nurses, which would make the statement that the staff consists of more male nurses than female nurses false.
Therefore, the speaker is a female nurse, as her exclusion does not affect the validity of the statements. 


  Posted by Dej Mar on 2012-10-23 01:24:55
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