Although the school board members agree there are

Responding to a PM on this question. The use of 'however' at the beginning of the sentence is an uncommon but acceptable use of however. In English, sentences can begin with 'however' + ',' to transition from one sentence to another: "I love riding my bike to work. However, I can't ride today because it is raining." The word 'however' in the example above gives the reader an indication that the 2nd sentence will work in opposition to the 1st sentence. Because this use case for 'however' shows a distinction between an earlier and later part, we don't see however used this way at the beginning of a sentence on the GMAT.

The use of 'however' in this GMAT question, however, [I couldn't help but stick this however in my post to show a comparison between what I said earlier and what I'm about to say] is to show the relative unimportance of magnitude. It's not really 'however' but rather 'however much'. You could state this phrase, 'however much', another way by saying 'regardless of how much': "Regardless of how much the school board members may agree that there are substantial inefficiencies in..." It's a use case that we don't see very often, but it is an appropriate use of however at the beginning of a sentence on the GMAT.

Hope that helps...

KW