A humble request – please give kudos if the explanation helps.
The answer is E.
First lets dissect the sentence.
1) The state board of education has directed assessments of schools in the highest populated districts,
This is the main clause of the sentence.
SV pair – (Board) is the subject and (has directed.) is the verb
2) with the decisive objective of decreasing the students who voice general unhappiness with the education in the schools.
This is the phrase in the sentence.
The core of this phrase is with the decisive objective of decreasing the students.
Students who voice… schools – who voice… schools is modifying the noun students correctly.
Note: decisive means Unmistakable/Determining or having the power to determine an outcome
The core sentence is: The… board… has directed assessments…, with the … objective of decreasing students…
A) with the decisive objective of decreasing the students who voice general unhappiness with the education in the schools
… decreasing the students… - this is incorrect since you cannot decrease the students. This is illogical.
(B) with the objective to decisively decrease the number of students who voice general unhappiness with the schools’ education
The meaning of the sentence is changed in this sentence. Because the objective is decisive not the decrease in number is decisive.
(C) decisively with the objective to decrease voicing of general unhappiness by the students with the school’s education
Decisively with the objective is incorrect.
The intent is to decrease the number of students who voice general unhappiness and not decrease voicing of general unhappiness.
This choice changes the meaning of the sentence.
(D) in a decisive attempt to reduce the number of students that ends up voicing general unhappiness with the schools’ education
This is a dependent clause since we have a subject and a verb pair in the sentence.
The subject is attempt and the verb is ends up.
But this changes the meaning of the sentence as: attempt ends up voicing general unhappiness.
(E) with the decisive objective of decreasing the number of students who voice general unhappiness with the schools’ education
This choice is correct. The meaning of the sentence is unchanged.
The answer is E.