All students at Pitcombe College were asked to label themselves conservative, liberal, or middle-of-the-road politically. Of the students, 25 percent labelled themselves conservative, 24 percent labelled themselves liberal, and 51 percent labelled 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 labelled themselves liberal endorsed what is generally regarded as a liberal position on that set of issues.
(B) More students who labelled themselves middle-of-the road than students who labelled themselves liberal opposed what is generally regarded as a liberal position on that set of issues.
(C) The majority of students who labelled themselves middle-of-the-road opposed what is generally regarded as a liberal position on that set of issues.
(D) Some students who labelled themselves conservative endorsed what is generally regarded as a liberal position on that set of issues.
(E) Some students who labelled themselves liberal endorsed what is generally regarded as a conservative position on that set of issues.

OA
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Conser------25%
Liberal------24%
Mid----------51%

On an issue 77% leaning towards liberal views

Lib + Mid 75% so a fraction of conservative endorsed liberal views than only 77% can be achieved.

Option D explains that

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All students at Pitcombe College were asked to label themselves conservative, liberal, or middle-of-the-road politically. Of the students, 25 percent labelled themselves conservative, 24 percent labelled themselves liberal, and 51 percent labelled 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.

No of Student who labelled themselves Conservative (C) = 25
No of Student who labelled themselves Middle (M) = 51
No of Student who labelled themselves Liberal (L) = 24

If all of the statements above are true, which one of the following must also be true?
(A) All students who labelled themselves liberal endorsed what is generally regarded as a liberal position on that set of issues.- Not always true as 25(C) + 51(M) + 1(L) can favor.Thus Incorrect.

(B) More students who labelled themselves middle-of-the road than students who labelled themselves liberal opposed what is generally regarded as a liberal position on that set of issues. Not always true as 25(C) + 51(M) + 1(L) can favor. Incorrect because more liberal students oppose.

(C) The majority of students who labelled themselves middle-of-the-road opposed what is generally regarded as a liberal position on that set of issues. Not always true as 25(C) + 51(M) + 1(L) can favor. Incorrect because more none of the middle-of-the-road opposed .

(D) Some students who labelled themselves conservative endorsed what is generally regarded as a liberal position on that set of issues.
Always True. Worst case scenario when 25(C) + 51(M) favor = 76 favor. The total favor count is 77, thus at least 1 from (L) must favor.

(E) Some students who labelled themselves liberal endorsed what is generally regarded as a conservative position on that set of issues.
A very nice Shell game option. Thus Incorrect

Hope this detailed explanation will be helpful for many.

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