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# All students at Pitcombe College were asked to label

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VP
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11 Dec 2012, 20:47
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Question Stats:

91% (02:27) correct 9% (01:39) wrong based on 131 sessions

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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.

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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How can I efficiently solve such questions under 1.5 minutes.
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11 Dec 2012, 21:57
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Marcab wrote:
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
[Reveal] Spoiler:
soon

How can I efficiently solve such questions under 1.5 minutes.

Hi Marcab ->

On the 1st read, given the stats ( 25% conservative , 24% liberal and 55% middle but 77% endorsed what is generally regarded as a liberal position) I came up with the following re-phrase - Some of the conservatives and some of the middle-of-the-road MUST have supported liberal position, otherwise 77% would not be possible). In these kind of Qs I try to find counter situations to kill the answer choices.

(A) All students who labelled themselves liberal endorsed what is generally regarded as a liberal position on that set of issues.
This need not be true : if all 25% conservatives + 55% middle of the road = 70% so 7% of liberal students could have endorsed liberal position on that set of issues. As we have found a counter situation, this answer choice is NOT correct (we are looking for MUST BE TRUE under all circumstances)

(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.
The red part is wrong. They supported the liberal position. The part before red is correct and must be true as we have only 49% (24+25) so more students must have come from middle-of-the road

(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
The red part is wrong. They supported the liberal position. The part before red is correct and must be true as we have only 49% (24+25) so majority (more than half) i.e 28% of 55% must have supported the liberal position.

(D) Some students who labelled themselves conservative endorsed what is generally regarded as a liberal position on that set of issues.
CORRECT. Matches re-phrase.

(E) Some students who labelled themselves liberal endorsed what is generally regarded as a conservative position on that set of issues.
This need be true as all the liberal students could have endorsed liberal position.

Pls do let me if find any reasoning / technique errors.

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19 Mar 2013, 02:33
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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.

Fame
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12 Dec 2012, 12:32
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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17 Dec 2012, 01:22
77% requires that all parties vote; however, none of the options is saying that.
Any choice that says a particular party (Lib, Cons, or Middle) votes would be correct-
D does that.

In the event Lib=26, the same logic will not apply since 26+51 = 77.
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Re: All students at Pitcombe College were asked to label   [#permalink] 17 Dec 2012, 01:22
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