25. The conclusion of this LSAT argument is extreme because of the word "no". The author assumes that Cecile's association is the only possible reason why Cecile might publicly disclose her investments. Choice (C) provides this assumption. Negation of the choice by adding "do NOT provide" weakens the argument, and thus (C) is a required assumption.
(A) refers to the future, but the conclusion is grounded in the present only -- "at this time".
(B) discusses conflict of interest, which is irrelevant -- the argument is only concerned with whether or not Cecile should disclose her investments at this time.
(D) might weaken the argument, but that's not what the question asks for.
(E) is irrelevant because the association's requirements are concerned with whether or not one sits on the board of a petrochemical company, not whether or not one owns investments in one.
26. The final question on this section of the LSAT asks for a parallel error. The structure of the original argument works this way: X (obesity - high-fat diets) is caused by Y (no nutrients), not by Z (too many calories). Thus, X's do not have Z. This same structure appears in choice (C): X (disorientation) is caused by Y (disruption of sunlight exposure), not by Z (sleep deprivation). Thus, X's do not have Z.
Choice (A) confuses correlation with causation -- you may quit reading (A) after the word "correlated" because correlation does not appear in the original argument.
(B) works this way: The belief that W's (sports fans) are X's (beer drinkers) is caused by Y (many beer commercials), not Z (stereotyping). Thus, most X's are W's.
Choice (D) works this way: W's (market crashes) are caused by Y's (rumormongering), not Z's (predicted downturns). Thus, Z's cannot be accurate. In the conclusion of (D), the Z's (predicted economic downturns) still exist (although not accurate), whereas in the original Z's do not exist.
(E) works this way: The preponderance of W's (math grads) among X's (programmers) is caused by Y (appropriateness of training), not Z (intelligence of math grads). Thus, greater than half of Y's have math training.