OFFICIAL ANSWER :
Identify the Question Type:
The question provides a set of circumstances that will be used to support the answer chosen. That makes this an Inference question. However, unlike most Inference questions, this one asks for something that must be false, rather than something that must be true. And it also must be false taking into account the additional condition in the question stem: if the defendant's chances are not weakened.
Untangle the Stimulus:
The stimulus gives some causal relationships. If Elvira Johnson testifies and a prestigious firm takes the case for the prosecution, then the defendant's chances will be weakened. Furthermore, Charles Chase will only testify if Elvira does and a prestigious firm does.
Predict the Answer:
If Chase cooperates, Elvira must testify and a prestigious firm must take the prosecution's case — the last sentence states these are the only conditions under which Chase will cooperate. Combine that with the first sentence: these conditions will greatly weaken the defendant's chances. Therefore, if, as the stem mandates, the defendant's chances are not greatly weakened, then Chase must not cooperate.
Evaluate the Choices:
(D) matches the prediction and is correct. It must be false, because if Chase cooperates, the defendant’s case would be weakened.
(A) is not necessarily false. The defendant's chances are weakened if Elvira testifies and a prestigious firm takes the case. If the defendant's chances are not weakened, Elvira could still testify -- there just wouldn't be a prestigious firm on the case.
(B) might be tempting at first; However, this is about chances. If the defendant's chances are weakened, he'll "most likely" get a longer sentence. However, even if the chances are not weakened, there's still a chance of a long sentence. It may not be "most likely," but it can't be ruled out.
(C) is not necessarily false. The defendant's chances are weakened if Elvira testifies and a prestigious firm takes the case. If the defendant's chances are not weakened, a prestigious firm could have still taken the case -- it may just be that Elvira didn't testify.
(E) only talks of Elvira possibly testifying; this would need to be known for sure (along with other information) to know if the defendant's chances are weakened, so this is incorrect.
TAKEAWAY: The right answer here depended on an important aspect of cause and effect relationships. If a cause always leads to an effect, then knowing that the effect didn't happen means that the cause didn't happen either.