Sentence Correction

Dr. Hakuta's research among Hispanic children in the United States indicates that the more the children use both Spanish and English, their intellectual advantage is greater in skills underlying reading ability and nonverbal logic.
(A) their intellectual advantage is greater in skills underlying reading ability and nonverbal logic
(B) their intellectual advantage is the greater in skills underlaying reading ability and nonverbal logic
(C) the greater their intellectual advantage in skills underlying reading ability and nonverbal logic
(D) in skills that underlay reading ability and nonverbal logic, their intellectual advantage is the greater
(E) in skills underlying reading ability and nonverbal logic, the greater intellectual advantage is theirs

I know B & D are wrong because it doesnt use the correct idiom "The more ... the greater "
Is advantage is the greater in skills underlaying in B wrong .
Is the fragment wrong because there no such word as underlaying or is it because underlaying changes the meaning

What about (D) in skills that underlay reading ability
is "underlay" the part tense of underlie ?


Also is 'X underlying Y " different from "X that underlies Y " ?