There is no need for a video explanation here because the question does not contain any major visual aspects. Please follow along the written explanation below:
So, let's break down this argument:
"In Sheldon most bicyclists aged 18 and over have lights on their bicycles,"
Q1: 18+-most-L L-some-18+
"most bicyclists under the age of 18 do not."
Q2: >18-most-not L not L-some->18
"It follows that in Sheldon most bicyclists who have lights on their bicycles are at least 18 years old."
C: L-most-18+ 18+-some-L
So what's the flaw here?
As you can see in "Q1," we do not know that MOST bicyclists in Sheldon that have lights on their bikes are at least 18 years old. We can only definitively say that SOME bicyclists in Sheldon that have lights on their bikes are at least 18 years old.
Remember that a quantifier does not have a contrapositive. We can, however, switch the variables of the quantifier statement and make a "most" into a "some." We cannot keep the "most" and switch the sides of the variables like the argument has done.
Answer choice (C) has the same issue:
"Most of the residents of Sheldon who voted in the last election are on the Conservative party's mailing list"
Q1: VLE-most-ML ML-some-VLE
"most of Sheldon's residents who did not vote are not on the list."
Q2: not VLE-most-not ML not ML-some-not VLE
"It follows that most of the residents of Sheldon on the Conservative party's mailing list voted in the last election."
C: ML-most-VLE VLE-some-ML
As you can see, the conclusion of (C) has merely switched the variables of Q1 without switching the "most" into a "some," which is the same error as the argument in the passage.
Hope that clears things up! Please let us know if you have any other questions.
paticandelarioAugust 7, 2017
In cases of questions like these, is it best to skip and come back? I find myself taking so long diagramming these.
estherJuly 5, 2018
I dont understand this statement in your explanation
"As you can see in "Q1," we do not know that MOST bicyclists in Sheldon that have lights on their bikes are at least 18 years old. We can only definitively say that SOME bicyclists in Sheldon that have lights on their bikes are at least 18 years old"
how come we do not know that MOst are at least 18.
ChristopherJuly 6, 2018
@paticandelario, there's no definite "best" strategy when it comes to these. I will say that the test makers like to be jerks and put these in the last 5 questions or so to make you burn time and speed through the last 3-5 questions. From personal experience, I would skip these, do the last few, and then finish this without the time pressure.
@esther, from the information given, we don't know how many bicyclists are 18 and over or 18 and under. We know that most 18+ bicyclists have lights. We know that most 18- bicyclists do not (which means that SOME do). However, there could be only ten 18+ bicyclists and one hundred 18- bicyclists. That means that MOST 18+ could be 6 cyclists total and SOME 18- could be 49.
In that case, we can safely say that SOME of the bicyclists with lights are over 18, but we cannot say MOST. With the given information, it's not possible to conclude that definitively.
