Data Sufficiency

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.

I also say B is the answer.

rishianand7 wrote: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.

This is an EITHER/OR group problem.
A new employee is EITHER a responder OR an administrator.
A new employee EITHER has had a physical previously OR has not.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.

Let R = responder, A = administrator, P = has had a physical previously, NP = has not had a physical previously.
Here's the grid:

In the grid above, the entries in any given row or column must add up to the TOTAL of that row or column.

Since the fractions in the problem are 3/4, 1/6, and 1/3, and the LCM of 4, 6 and 3 = 12, let the total number of new employees = 12x.
Since 6 of the new employees require physicals -- and the only type of new employee who requires a physical is a responder who has not had a physical previously -- the number of responders who have not had a physical previously = 6.
Since 3/4 of the new employees are responders, the total number of responders = (3/4) * 12x = 9x.
Entering these values into the grid, we get:


To determine the total number of new employees -- 12x -- we need to know the value of x.
Question rephrased: What is the value of x?

Statement 1: 1/6 of the new employees are administrators who have had a physical in the previous year.
Since (1/6) * 12x = 2x, we get:

No way to solve for x.
INSUFFICIENT.

Statement 2: 1/3 of the new responders have had a physical in the previous year.
Since the total number of new responders = 9x, the number of new responders who have had a physical previously = (1/3) * 9x = 3x.
Here's the resulting grid:

Since 6x=6, x=1.
Thus, the total number of new employees = 12x = 12*1 = 12.
SUFFICIENT.

The correct answer is B.