I could say, it's checking for 'Rhetorical construction'. I mean, how 'claims' should be used in sentence.
As per correct grammatical construction, 'claims' must be followed by 'that' or 'to be', no phrase or clause in between...

Therefore only one option left, that is [spoiler]'D'[/spoiler]

thanks for presenting an OG example. This questions tests the following, mainly 1 and 2

1. I concur with previous posters, such constructions are popularly referred to as "Subjunctives" and have key word such as claim, require, etc..such key words should be followed by "that" or an infinitive "to be"..these constructions never have "should"-just for additional information

1. usage of essential and non-essential modifiers: from a one page writing sample is certainly NOT the essential part and hence can be set off in a pair of commas used as a non-essential modifier

2. for idiom lovers: able to or ability to is correct usage,

Is the sentence not trying to state: "be able to assess from a one page writing sample more than 300 personality traits"