Statement 1:
Since m+c = 50%, total male + total custodial = 50% of 120 = 60.

The following cases satisfy BOTH STATEMENTS.

Case 1: total male = 30, total custodial = 30


Case 2: total male = 50, total custodial = 10


In Case 1, the number of non-custodial females = 86.
In Case 2, the number of non-custodial females = 66.
Since the number of non-custodial females can be different values, INSUFFICIENT.

The correct answer is E.

AndreiGMAT wrote:In an office that employs 120 people, m% of the employees are male, and c% of the employees are members of the custodial staff. How many employees are females who are not members of the custodial staff?

(1) m + c = 50

(2) The number of female employees who are members of the custodial staff is four

Statement 1:

It's tempting to take this statement to mean that if m + c = 50 then 50% are not male or members of the custodial staff and are therefore females who are not members of the custodial staff, making this statement sufficient.

However, all of the members of the custodial staff could be men, in which case, m = 25 and c = 25 and they are the same people, meaning that 75% of the employees are females who are not members of the custodial staff.

Alternatively, there could be no overlap between m and c, meaning that various scenarios are possible, including the following one.

m = 50 c = 0 females not custodial = 50%

There could also be various degrees of overlap of m and c. So females who are not members of the custodial staff can range from 50% to 75%.

Insufficient.

Statement 2:

From this we have no idea how many female employees there are.

Insufficient.

Statements Combined:

Given the information in the combined statements we still don't know how much overlap there is between m and c.

While m and c cannot completely overlap given the information in statement 2, they could still overlap some or none, as in the following examples.

females custodial = 4/120 = 3.33%

Some Men Custodial: m = 25 c = 25 m and c overlap = 21.66% females custodial = 3.33% females not custodial = 71.66%

No Men Custodial: m = 46.66 c = 3.33 m and c overlap = 0 females custodial = 3.33% females not custodial = 50%

Insufficient.

The correct answer is E.