Logical Reasoning

PT155 · S2 · Q9 Rodents are small, gnawing mammals

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Rodents are small, gnawing mammals characterized by their chisel-like incisor teeth.

Information

Since we read Must Be True looking primarily for Conditional, Math-y, or Causal ideas, we would be most attracted to the two Most claims.

Most NA mammal species are not rodent species. but Most individual mammals in NA are rodents.

Evaluate

There are a couple famous inferences we can make with two Most statements, but this example is neither of them. (Here they are, for reference, though)

Most A's are B Most A's are B Most A's are C Most B's are ~A infer: Some B's are C more B's than A's

However, we can tell that we're supposed to do something mathematical by reconciling those two most claims.

It's sort of a paradox -- GIVEN THAT most species are not rodent species, HOW CAN IT BE most individuals are rodents?

Let's pretend we're at a restaurant that forbids co-ed seating. It's either all men eating at a table together or all women eating at a table together.

What could we infer from this pair of statements? Most of the tables are not female-tables. but Most of the individual people eating at the restaurant are females.

If women are responsible for a minority of tables at the restaurant but a majority of people at the restaurant, then there must be more women sitting per table.

10 tables with 5 women each = 50 women 12 tables with 4 men each = 48 men

Out of the 22 tables, most of them aren't female tables (10 of 22), but out of the 98 individuals, most of them are females (50 of 98).

Goal

Similarly, if most species aren't rodents, but most individuals are rodents, then there must be more rodents per rodent species than there are non-rodents per non-rodent species.

(Just like there were more women per female-table than there were men per male-table ... also, my apologies to womankind for making them the rodents in this math metaphor)

9.

Which one of the following is most strongly supported by the information above?

  1. Most species of North American

    Too Strong: most species

    We know that rodents have chisel-like incisor teeth, but we're also told that most species of NA mammals aren't rodents. If we knew that most species were rodents, we could infer this answer.

    5% picked this

  2. Correct

    In North America, rodent species

    Why this is right

    This is giving us the mathematical inference we predicted: if most species are not rodent, but most individuals are rodent, then there must be more rodents per rodent species than there are non-rodents per non-rodent species. If most of the vehicles at a drive-in were trucks, but most of the people at the drive-in arrived in a car, then you could infer that there tended to be more passengers per car than there were per truck.

    Skill tested: Most Supported · how this choice captures the argument's function is the move to repeat next time.

    71% picked this

  3. Most species of mammals that

    Unknown Group

    We don't have any information about 51% or more of "mammals with chisel-like incisor teeth". We know about most "NA mammal species" and most "NA individual mammals", and those are the only most groups we know about.

    3% picked this

  4. Of the mammal species in

    Too Specific: the single #1 highest

    In each of our two math metaphors so far (male/female tables at restaurant ... or people who came to the drive-in via truck vs. car), we only know something about the overall average. We can't get as specific as one specific table, one specific vehicle. It could be that the table with the most people at it was a male-table, but all the other male-tables only had two dudes, whereas the female-tables were averaging like 5 per table. It could be that the vehicle with the most passengers at the drive-in was an unsafe pickup truck carrying 15 people in the flatbed, but all the other trucks just had 2 passengers, whereas the cars were averaging like 5 people per vehicle. In other words, there can definitely be an outlier among males / trucks / non-rodents. Our inference is only about the overall total vs. number of groups, so our inference has to be expressed as an average of individuals per group.

    19% picked this

  5. Most nonrodent mammal species can

    Unknown Group

    We don't have any information about 51% or more of "nonrodent mammals". We know about most "NA mammal species" and most "NA individual mammals", and those are the only most groups we know about. You can't ever derive a fact about "most X" if you were never told a fact about "most X".

    2% picked this

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