Bunuel wrote:
In a real estate office that employs n salespeople, f of them are females and x of the females are new employees. What is the value of n ?
(1) If an employee were randomly selected from the n employees, the probability of selecting a female would be 2/3.
(2) If an employee were randomly selected from the f female employees, the probability of selecting a new employee would be 1/2.
NEW question from GMAT® Official Guide 2019
(DS03999)
As all we're given are variables, we'll pick simple numbers to help make things concrete.
This is an Alternative approach.
(1) Say that f = 10. Then there are 3/2 * 10 = 15 employees. Clearly, if there is a different number of females there will be a different number of employees.
Insufficient.
(2) Say, again, that f = 10. Then x = 10 * 1/2 = 5 are new employees. We have no way to calculate n so this cannot be sufficient.
Insufficient.
Combined:
Combining the statements doesn't help much: if we pick f = 10, then we get the same values as above and if we pick f = 20 we get values twice as large. As there are no additional constraints in the question we cannot determine the value of n.
Insufficient.
(E) is our answer.
Note that a shorter, Logical approach would be to notice that we are asked to give a specific number but not given any numbers to start with. That means we cannot answer.