Sentence Correction

Final solution at one place:

Important: The purpose of this post (and all the other posts by me) is to give a complete solution to all GMAT-Prep Verbal questions at one place. Sometimes students have to wade through dozens of posts to get to the final answer. My posts will give one complete and crisp solution required to arrive at the correct answer by eliminating the wrong one. Some of the content in these posts may have been taken from various other sources (discussion forums).

Several educational research groups are denouncing the mayor's proposal of a system by which individual teachers would be given raises or bonuses should it be that test scores show their students' mastery of reading skills having improved over a nine-month period.
(A) should it be that test scores show their students' mastery of reading skills having
(B) should it be that test scores show their students' mastery of reading skills have
(C) should test scores showing their students' mastery of reading skills has
(D) if test scores showing their students' mastery of reading skills having
(E) if test scores show that their students' mastery of reading skills has

The use of 'should' (in the conditional sense) is considered wrong on the GMAT. This is typically old-style British usage. This eliminates A, B, and C.

The 'if' part of a conditional sentence definitely needs a verb (as it is a dependent clause). Choice D doesn't contain a verb (the word 'having' is not a verb ... in fact, -ING form alone (without a preceding helping verb) are not verbs at all. D is wrong for this reason.

E is correct. It also uses the correct subject verb agreement (mastery ... has).