A significant number of Qualitex Corporation’s department heads are

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.