"Good hunter" and "bad hunter" are standard terms in the study of cats. Good hunters can kill prey that weigh up to h...

Naz on September 24, 2014

Let's diagram the stimulus.

"All good hunters have a high muscle-to-fat ratio,"

PR: GH ==> M2FR
not M2FR ==> not GH

"Most wild cats are good hunters."

Q1: WC-most-GH
GH-some-WC

"some domestic cats are good hunters as well."

Q2: DC-some-GH
GH-some-DC

We know that we cannot combine a "most" statement with a "some" statement. But, we can combine a Sufficient & Necessary statement with a Quantifier statement.

Remember, as long as the right-hand side variable of a "most" or "some" statement is the same as the sufficient condition of a Sufficient & Necessary statement, then we can combine the two statements.

So, we can combine "Q1" with "PR" like so:

WC-most-GH ==> M2FR

From this we can conclude: "WC-most-M2FR," which reads: "Most wild cats have a high muscle-to-fat ratio."

We can also combine "Q2" with "PR" like so:

DC-some-GH ==> M2FR

From this we can conclude: "DC-some-M2FR," which reads: "Some domestic cats have a high muscle-to-fat ratio."

You cannot assume that just because most wild cats have a high muscle-to-fat ratio and some domestic cats have a high muscle-to-fat ratio that a smaller number of domestic cats than wild cats have a high muscle-to-fat ratio; we do not know how many wild cats and how many domestic cats there are.

Let's say there are 100 domestic cats and 10 wild cats. We could have 6 wild cats with a high muscle-to-fat ratio, i.e. more than half of them have a high muscle-to-fat ratio. We could also have 10 domestic cats with a high muscle-to-fat ratio, i.e. at least one of the domestic cats has a high muscle-to-fat ratio. In this example, it is not true that a smaller number of domestic cats (10) than wild cats (6) have a high muscle-to-fat ratio.

Don't fall for the percentage/number trap. Since we do not know how many of each cat there is, we cannot infer relative numbers from mere ratios.

Answer choice (D) states: "Some cats that have a high muscle-to-fat ratio are domestic."

This is exactly one of the inferences we made above by combining "Q2" and "PR." We know by combining these two statements that some domestic cats have a high muscle-to-fat ratio. Thus, answer choice (D) must be true.

Hope that clears thing up! Please let us know if you have any other questions.

shafieiava on January 23, 2020

@Naz I used the same set up you had above but accidentally fell into choosing answer choice C. Is answer choice C incorrect because it is a faulty application of the contrapositive of the first premise (e.g. do not just negate?) Thanks in advance.

Emil-Kunkin on April 12, 2023

I think that is the issue with C indeed, I think there is a mistaken reversal. Perhaps there is a cat that is a bad hunter that does not have a low ratio, but is a bad hunter for some other reason, like blindness