E is my choice.
(A) The new council must have the support of the nationâ€™s labor leaders if it is to succeed - we are not sure whether out man will be able to get the support. so this is out.
(B) During his years as a labor leader, Grayson established a record of good relations with business leaders - how do we know that even now those good relations are intact? OUT
(C) The chair of the new council must be a person who can communicate directly with the leaders of the nationâ€™s largest labor unions - We are not sure whether our man will be able to do that - so OUT.
(D) Most of the other members of the new council will be representatives of business management interests - SO???
(E) An understanding of the needs and problems of labor is the only qualification necessary for the job of chairing the new council - 'only qualification' gives it away! IF understanding is the only requirement, then our man will shine. SO KEEP THIS!!