We essentially need to find how the Company will not have to extend one department head over multiple departments.

A: No. Dheads will still retire. No gurantee.
B: Same reasoning as in A. No gurantee.
C: reducing employees will not do anything. Still too many departments and not enough Dheads.
D: same reasoning as C. still more departments than Dheads.


E: best answer. Says Dheads will equal departments.

A significant number of Qualitex Corporation’s department heads = N
are due to retire this year. = N is decreasing , but we need to keep N constant by adding values to it !!! let us assume that X person left so we need to add X to make it N

The number of employees other than current department heads
who could take on the position of department head is equal to only about half of
the expected vacancies. - the number available to be added is only X/2, we have to compensate the rest.
Oualitex is not going to hire department heads from
outside the company or have current department heads take over more than one
department,- X/2 cannot be increased from outside source.

this is the problem : now lets see the answer choice, what can be done to compensate the decrease

A - irrelevant
B - irrelevant, the heads are retiring not leaving because their compensation is low
C - Oualitex is not going to hire department heads from
outside the company or have current department heads take over more than one
department - this is a company policy so cannot be changed,
even if it hired it wont solve the problem at hand.
D - irrelevant
E - yes !!! it is it
from the above understanding :
N department ---- N heads...( this is decreasing to N - X )
now if we decrease the number of departments the problem will be solved !!
N-X departments ---- N-X heads
Hence, E is correct.
_________________

A significant number of Qualitex Corporation’s department heads are due to retire this year. The number of employees other than current department heads who could take on the position of department head is equal to only about half of the expected vacancies. Oualitex is not going to hire department heads from outside the company or have current department heads take over more than one department, so some departments will be without department heads next year unless Qualitex ______.

Boil it down - Number of employees who could take on position of department head is equal to only about half of the expected vacancies
- not hire from outside or have 1 head handle more than 1 departments
- So some departments will be without heads unless __________

A. promotes some current department heads to higher-level managerial positions - Irrelevant - in this case we will have greater number of departments without heads
B. raises the salary for department heads - Irrelevant
C. reduces the number of new employees it hires next year - Irrelevant
D. reduces the average number of employees per department - Irrelevant - the number of departments and number of heads does not change
E. reduces the number of its departments - Correct

Answer E
_________________

Please explain your answer.
A significant number of Qualitex Corporation’s department heads are due to retire this year. The number of employees other than current department heads who could take on the position of department head is equal to only about half of the expected vacancies. Oualitex is not going to hire department heads from outside the company or have current department heads take over more than one department, so some departments will be without department heads next year unless Qualitex ______.

A. promotes some current department heads to higher-level managerial positions -Even if the company promotes the existing heads to upper positions, the number of departments will remain the same. Incorrect.
B. raises the salary for department heads -Salary is irrelevant.
C. reduces the number of new employees it hires next year -Even if it doesn't hire new employees, the number of departments wouldn't change
D. reduces the average number of employees per department -Avg. number of employees is out of scope
E. reduces the number of its departments -Correct. If the number of departments reduce then the vacancies will surely reduce.

Very crisp and clear explanation gmatexam439
I got this question correct too

A. promotes some current department heads to higher-level managerial positions - Not relevant as department heads shall still retire and regardless of promotions the number of departments shall not change
B. raises the salary for department heads - Raising the salary is out of scope as it shall have no impact on future vacancies
C. reduces the number of new employees it hires next year - Irrelevant as Hiring or not hiring number of new employees shall not have an impact on number of vacancies
D. reduces the average number of employees per department - Irrelevant - the number of departments and number of heads does not change - Not relevant as average number of employees is not what we are concerned.
E. reduces the number of its departments - [b]Correct as reducing the number of departments would reduce the number of vacancies[/b]

is head of department not an employee??? why D is wrong???