Let us first dissect the sentence.
Psychological studies have found that - Here that introduces a clause
children
who are afflicted with Attention Deficit Disorder (ADD) – This is a restrictive clause
are difficult to teach, inattentive, and unable to sit still for very long.
SV pair – Children are
We have a parallel list difficult to teach, inattentive, and unable to sit still.
(A) that children who are afflicted with Attention Deficit Disorder (ADD) are difficult to teach, inattentive, and
This choice appears to be correct.
(B) that children who are afflicted with Attention Deficit Disorder (ADD) are difficult to teach, inattentive, and are
And are is incorrect in this parallel list.
(C) children who are afflicted with Attention Deficit Disorder (ADD) are difficult to teach, inattentive, and they are
Ans they are is incorrect in this parallel list. Found that is missing in this choice.
(D) children who are afflicted with Attention Deficit Disorder (ADD) are difficult to teach, and inattentive, and they are
Ans they are is incorrect in this parallel list. And inattentive is incorrect since we have a list of three elements and and should appear before the third and last element in the list. Found that is missing in this choice.
(E) that children who are afflicted with Attention Deficit Disorder (ADD) are difficult to teach, they are inattentive, and are
they are inattentive, and are – is incorrect in the list for reasons stated above.
Answer is A.