Question on LSAT question

mzoodle

" Most people who shop for groceries no more than 3 times a month buy prepared frozen dinners regularly. In Hallstown, most people shop for groceries no more than 3 times a month. Therefore, in Hallstown most people buy prepared frozen dinners regularly".

Why is this an invalid argument?

Alex

@mzoodle said:
" Most people who shop for groceries no more than 3 times a month buy prepared frozen dinners regularly. In Hallstown, most people shop for groceries no more than 3 times a month. Therefore, in Hallstown most people buy prepared frozen dinners regularly".

Why is this an invalid argument?

The problem with this argument is that we can't properly infer if the "most people" in the general population applies to the "most people" in Hallstown.

LSATcantwin

Think of it in numbers.

Most people who shop for groceries no more than 3 times a month buy prepared frozen dinners regularly.

Say 100 people shop for groceries no more than 3 times a month. So 51 of them buy prepared frozen dinners regularly.

Okay so that's 49 people who DON'T buy the prepared frozen dinners regularly and,
That's 51 people who DO buy the prepared frozen dinners regularly.

40 of the 49 people who DON'T buy the dinners regularly live in Hallstown
3 of the 51 people who DO buy the prepared frozen dinners regularly live in Hallstown.

Do most of the people who live in Hallstown buy prepared frozen dinners?

Hallstown population of 43. 40 of them shop for groceries less than 3 times a month but DON'T buy prepared frozen dinners. 3 of them shop for groceries less than 3 times a month and DO buy prepared frozen dinners.

BinghamtonDave

As an aside, it is the preferred method of these forums to link to the question with the following framework: PT number/Section number/question number. For this particular question it would be: PT 32 Section1 Question 22.

Now, more specifically, this question posits invalid argument form number 6.
https://7sage.com/lesson/invalid-argument-form-6-of-7/

Why is this invalid? Because the two sets given might not have an overlapping region. The second set might be a much, much larger set than the first, and therefore the "most" that the first set is in might not be in the "most" section of the second set. That is quite a mouthful, so lets look at an example.

Think about it like this:
-most of my family members speak english (9 out of 12 of my family members speak English)
-most people who speak english are not Americans (roughly 850 million out of 1.1 billion)
therefore most of my family members are not Americans

The core issue here is that most of my family members fall within the 250+ million people who do speak english and who are Americans. An valid argument form will not put us into this position.

We see that:
A----most----->B----most---->C
A-----most---->C
does not follow in the above example.

I hope this example helps
David

Numbers are rough estimates obtained from the following (not perfect) source:
https://en.wikipedia.org/wiki/List_of_countries_by_English-speaking_population