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The fire department has two classes of employees, responders

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The fire department has two classes of employees, responders [#permalink] New post 18 Dec 2012, 06:06
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The fire department has two classes of employees, responders and administrators. The department requires a physical for each new employee, unless that employee has had a physical in the previous year or is an administrator. Last month, the fire department required physicals of 6 new employees. If 3/4 of the new employees are responders, how many new employees does the department have?

(1) 1/6 of the new employees are administrators who have had a physical in the previous year.
(2) 1/3 of the new responders have had a physical in the previous year.
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Re: The fire department has two classes of employees, responders [#permalink] New post 18 Dec 2012, 06:24
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The fire department has two classes of employees, responders and administrators. The department requires a physical for each new employee, unless that employee has had a physical in the previous year or is an administrator. Last month, the fire department required physicals of 6 new employees. If 3/4 of the new employees are responders, how many new employees does the department have?

Since out of new employees only responders who didn't have a physical in the previous year will need a physical, then the number of new repsonders who didn't have a physical in the previous year = 6.

(1) 1/6 of the new employees are administrators who have had a physical in the previous year. Not sufficient.

(2) 1/3 of the new responders have had a physical in the previous year. This implies that 2/3 of the new responders have NOT had a physical in the previous year. As 3/4 of the new employees are responders, then 3/4*(# of new employees)=(# of new responders) and 2/3*(# of new responders)=6 --> 2/3*3/4*(# of new employees)=6 --> (# of new employees)=12. Sufficient.

Answer: B.
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Re: The fire department has two classes of employees, responders [#permalink] New post 18 May 2014, 03:53
Statement #1: 1/6 of the new employees are administrators who have had a physical in the previous year.
New administrative employees do not need physicals, regardless of whether they have had a physical in the past year or not. All new employees needing new physicals are responders. This information is irrelevant.
This statement, alone and by itself, is insufficient.

Statement #2: 1/3 of the new responders have had a physical in the previous year.
There are six new employees that needed physicals, and all of them must be new responders. This six is the one-third of responders that needed physicals, so 2/3, 12 new responders didn't need physicals. There are 18 new responders in total, which accounts for 3/4 of all new employees, so there are 24 new employees.
This statement, alone and by itself, is sufficient.

Hence B.
Re: The fire department has two classes of employees, responders   [#permalink] 18 May 2014, 03:53
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