Critical Reasoning

All students at Pitcombe College were asked to label themselves conservative, liberal, or middle-of-the-road politically. Of the students, 25 percent labeled themselves conservative, 24 percent labeled themselves liberal, and 51 percent labeled themselves middle-of-the-road. When asked about a particular set of issues, however, 77 percent of the students endorsed what is generally regarded as a liberal position.

If all of the statements above are true, which one of the following must also be true?

(A) All students who labeled themselves liberal endorsed what is generally regarded as a liberal position on that set of issues.
(B) More students who labeled themselves middle-of-the road than students who labeled themselves liberal opposed what is generally regarded as a liberal position on that set of issues.
(C) The majority of students who labeled themselves middle-of-the-road opposed what is generally regarded as a liberal position on that set of issues.
(D) Some students who labeled themselves conservative endorsed what is generally regarded as a liberal position on that set of issues.
(E) Some students who labeled themselves liberal endorsed what is generally regarded as a conservative position on that set of issues.

This question seems a very good example for learning the use of quantity words(such as many, some, majority) usage. Let's discuss this question I will disclose OA later.

Id think this is one where you can use basic math to get the right answer.

The question tells us that 77% of all students endorsed the liberal position. If all liberal (24%) and all middle of the road (51%) endorsed the position that is only 75% of all students. Thus at least 2% of conservatives had to support the liberal issue. That is what is given as choice D which is the correct answer as it is the only choice that must be true.

Going through the others

A) does not have to be true. If all middle and all conservative support it thats 76%, so only 1% of supports have to be liberal

B) might be true or it might not be true.

C) This says a majority of middle of the road opposed the idea. That would mean at least 26 middle of the road people opposed the idea while no more than 25 supported it. This cant be true to reach 77%. If 26 said no to the issue that would mean a max of 74% agreed with the issue.

E) could be true or might not be true.

Originally set of looking for an answer that showed the middle of the road folks supporting the liberal proposal but since I could not find that, I picked D and it's really quite easy:

Assume the total people to be 100 (as one may do in quant)
Add up the facts that 100% of both Middlers and Liberals supported the measure and you have 76% which is 1% short of the 77% who supported the measure hence it must be true that at least 1% of conservatives supported the measure.

D states the same and hence is the answer.