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# All students at Pitcombe College were asked to label

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02 Apr 2015, 08:20
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11
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Difficulty:

45% (medium)

Question Stats:

69% (02:11) correct 31% (02:17) wrong based on 615 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.

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25 May 2015, 07:52
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Unable to understand this question.
Initally 25% said they are conservative , 24% liberal , and 51 % said Middle.
But with specific set 77% of them gave answer which is considered as liberal ..
Is my understanding of premise correct ?

Yes, your understanding of the premise is absolutely correct.

Reason:
Those who support i.e. liberal = 24%
Those who don't support i.e. conservative = 25 %
Those who are in the "Maybe" zone = 51%

Now, when specific set is given, 77% of the total support the issue i.e. they are liberal.
When we look at the figures above, what can we assume??

We have to consider the maximize condition here.
Say, all of the 24% of liberal guys support the specific set of issue and all of the "Maybe" zone guys also support the issue, then the total percentage of people supporting he issue will be 24% + 51% = 75%. The value is still short by 2%. So the remaining 2% must have come from the guys who are conservative.

##### General Discussion
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02 Apr 2015, 10:21
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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.Not necessarily. Maybe 25(all conservative)+51(middle of the road)+1(liberal), that is one 1% liberals endorsed this

(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.Maybe all 23 of those who opposed the liberal stand were "liberals" in the initial survey. This would mean none of the "middle of the road" opposed the stand

(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.Maybe all the "conservatives" of the initial survey were the 23 who opposed the liberal stand, hence none of the "niddle of the road" opposed the liberal stand

(D) Some students who labelled themselves conservative endorsed what is generally regarded as a liberal position on that set of issues.Firstly, I think this should be "atleast some". I initially rejected this option because of this small nuance. Otherwise this option is good. Now even if we consider that all the "liberals" and "middle of the road" voted in favour of the liberal stand, they would add up to 24+51=75; therefore, 2 of the "conservatives" voted in favour of the liberal stand. Another scenario could be that ALL "conservatives" voted in favour of the liberal stand. So we are looking at a range of 2(categorised as "some) to 25 (categorised as "all")

(E) Some students who labelled themselves liberal endorsed what is generally regarded as a conservative position on that set of issues.OFS. We are not given any conservative issue's statistics to analyse.
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25 May 2015, 02:13
Unable to understand this question.
Initally 25% said they are conservative , 24% liberal , and 51 % said Middle.
But with specific set 77% of them gave answer which is considered as liberal ..
Is my understanding of premise correct ?

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23 Sep 2016, 08:57
this question can be solved by use of mathematical logic (venn diagrams possibly)
as the students have to take one of the 3 possible stands conservative, liberal, or middle-of-the-road politically, it means neither value is 0 %
only conservative = 25 %
only liberal = 24 %
but there is a contradiction " 77 percent of the students endorsed what is generally regarded as a liberal position "
now if we consider the worst case scenario that middle-of-the-road politically and only liberal support the position
i.e. 51% + 24 % = 75 %
we are still short 2 % which would have definitely come from the only conservative students
option D states exactly what we are trying to deduce and so its the correct answer

+1 kudos if you like the solution
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30 Jul 2017, 04:15
AmoyV 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.Not necessarily. Maybe 25(all conservative)+51(middle of the road)+1(liberal), that is one 1% liberals endorsed this

(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.Maybe all 23 of those who opposed the liberal stand were "liberals" in the initial survey. This would mean none of the "middle of the road" opposed the stand

(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.Maybe all the "conservatives" of the initial survey were the 23 who opposed the liberal stand, hence none of the "niddle of the road" opposed the liberal stand

(D) Some students who labelled themselves conservative endorsed what is generally regarded as a liberal position on that set of issues.Firstly, I think this should be "atleast some". I initially rejected this option because of this small nuance. Otherwise this option is good. Now even if we consider that all the "liberals" and "middle of the road" voted in favour of the liberal stand, they would add up to 24+51=75; therefore, 2 of the "conservatives" voted in favour of the liberal stand. Another scenario could be that ALL "conservatives" voted in favour of the liberal stand. So we are looking at a range of 2(categorised as "some) to 25 (categorised as "all")

(E) Some students who labelled themselves liberal endorsed what is generally regarded as a conservative position on that set of issues.OFS. We are not given any conservative issue's statistics to analyse.

While selecting D as the answer are we not assuming that "middle of the road" voted in favour of the liberal stand because it is nowhere mentioned in option D. While i read option D my liberal count came out to be 24+25 which is not equal to 71.
Eventually, i did not select any answer option because my total did not reach 71 until i assume something, but do we really need to assume this far that all "middle of the road" voted in favour of the liberal stand?
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31 Oct 2018, 04:40
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Re: All students at Pitcombe College were asked to label   [#permalink] 31 Oct 2018, 04:40
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