#26 - The older a country is, the more likely it is to be

[Administrator]

Complete Question Explanation

Parallel Reasoning. The correct answer choice is (D)

This is an exceedingly difficult question. In the stimulus, the author provides a rule, a fact that
invokes the rule, and a strange conditional conclusion. The rule is provided in the first sentence, that
“the older a country is, the more likely it is to be ruled by a monarch.” The fact provided is that most
countries are not ruled by monarchs. From this information, the author concludes that “if a country is
particularly new it is probably not ruled by a monarch.”

This likely was not the conclusion that you were expecting. A more predictable conclusion would
have been that it is probably the case that most countries are not old. However, the rule only dealt
with the increasing probability that a country will be ruled by a monarch as it grows older. The
rule told us nothing about the initial probability of a country being ruled by a monarch. So, if the
probability of a new country being ruled by a monarch is 95 percent, it would be likely that most
countries would have monarchs. Since we are told that most countries do not have monarchs,
then it must not be likely that a new country will have a monarch, in keeping with the argument’s
conclusion.

This is a Parallel Reasoning question. Our prephrase is that the correct answer choice will contain an
argument with the same logical structure as that in the stimulus, with a probabilistic conclusion that
results from the consideration that the argument’s rule addresses an increasing probability from an
uncertain starting point.

Answer choice (A): This answer choice is incorrect because the conclusion discusses the popularity
of a movie as opposed to the popularity of a novel.

Answer choice (B): Here, the fact provided in the first sentence of the argument is the reverse of
what is required for the argument to match the argument in the stimulus. Here, the fact should state
that “most movies are not based on novels.”

Answer choice (C): In this case, the argument’s conclusion does not match the conclusion from the
stimulus. This answer choice has switched the opening rule (matching what was in the first sentence
of the stimulus) with the rule provided in the conclusion.

Answer choice (D): This is the correct answer choice, because the argument it contains matches
the logical structure of the argument in the stimulus. The argument provides a rule (“the more
popular a novel is, the more likely it is to be made into a movie”), a fact that implicates that rule
(“most novels are not made into a movie”), and then a conclusion that matches the conclusion in
the stimulus. Here, since most novels are not made into a movie, it must be the case that if a novel
is unpopular it will not be made into a movie. Otherwise, if even unpopular novels were likely to be
made into a movie, then most novels would be made into movies, which we know is not the case.
This certainly is a difficult question and a difficult answer choice, and if you had difficulty with it,
then you are in good company.

Answer choice (E): Here, the rule stated in the conclusion provides the opposite of what is needed to
match the conclusion in the stimulus. In this case, the conclusion should state that “if a novel has a
particularly simple plot, it will probably not be made into a movie.”

[cecilia]

Honestly, by the time I got to this question, my brain was completely fried. I was nevertheless able to get to the right answer, tho it took me well over the allotted time. I struggled for a good length of time between D and E. Is (E) wrong because of the slight shift in the conclusion's content? Instead of saying it "will probably be made into a movie," should it have said "the more likely be made into a movie"? Would that have made it a better answer choice???

I initially diagrammed the stimulus because my head was already spinning and I felt it easier to be robotic and just do a matching game. Any ideas on the best way to have approached this question?

Thanks in advance Powerscore peeps!

[Robert Carroll]

Cecilia,

It's understandable that the last question of a section would be particularly difficult and time-consuming. Since this is a Parallel Reasoning question, you'd want a simple summary of the structure of the stimulus in order to notice as quickly as possible which answer choices alter that structure and which don't, so you can eliminate the former as wrong answer choices.

You are looking for "probably" or a synonymous thing in the conclusion, so if answer choice (E) said "more likely" it wouldn't have helped it. The conclusion in the stimulus is not saying "the newer, the more likely not to be ruled by a monarch." It just says that particularly new countries are probably not ruled by monarchs. Thus, this is not what answer choice (E) got wrong.

Answer choice (E) was wrong because it changed the relation in the stimulus - older means more likely something will happen. Answer choice (E) instead says that more complex means less likely something will happen. Only answer choice (D) maintains the structure in a parallel fashion.

Robert Carroll

[cecilia]

Thanks Robert!

[cecilia]

Hi Robert or any other Powerscore peeps:

Just a brief follow up on (E) . Was it also wrong because E's conclusion ended with a *positive* prediction - as in "it will probably BE made into a movie" as opposed to the original argument, which conclude with it probably WILL NOT be governed by a monarch.

Thanks in advance!

[Jon Denning]

Hey Cecilia - I think that's the main gist of it, yes. In the stimulus we have a relationship about increasing age and increasing likelihood of an occurrence, and a conclusion that goes in the other direction: decreasing age = decreasing likelihood. A positive (or direct) correlation, in effect.

(E) on the other hand does something different, as it presents a negative (or inverse) correlation: increasing complexity tells you decreasing likelihood of an occurrence (movie), and a conclusion that flips it to show little complexity = high likelihood of occurrence.

I hope that helps!

[JKP2018]

I solved this one using a very different approach to what is described here. I got it right, but I'm not sure if that was a coincidence or if I was on the right track.

Every answer choice says "Most novels are not made into movies," which corresponds to the "most countries are not ruled by monarchs" in the stimulus. Because that element is present in every answer, we can functionally ignore it.

The simplified stimulus thus says, basically, "if it is old, it is likely a monarchy; if it is not old, it is likely not a monarchy." If we diagram it, we get "A->B, therefore ~A->~B" (where ~A is 'not A'). Does an answer choice follow this structure? If I simplify each answer, they become

a) "If it is popular, it is likely a movie. If it is not popular, it is not a novel." (A->B, ~A->~C). Not a match.

b) "If a movie is popular, it is likely a based on a novel. If a novel is popular, it is likely made into a movie." (roughly B->A, so A->B). Not a match.

c) "If not popular, likely not made into a movie. If it is popular, likely made into a movie." (~A->~B, A->B.) Not a match.

d) "If it is popular, it is likely made into a movie. If it is unpopular, likely not made into a movie." (A->B, ~A->~B). MATCHED!

e) "If it is complex plot, likely not made into a movie. If it is not a complex plot, likely made into a movie." (A->~B, ~A->B). Not a match.

So I got the answer, but it was quite different, and I didn't think about probability or the validity of the conclusion at all, and if this is not a reliable way to approach such questions, I don't want to rely on it.

[James Finch]

Hi JKP,

Your approach looks sound, as you identified that the conclusion of the stimulus was essentially a Mistaken Negation of the conditional relationship given by the premises, as well as the functional irrelevancy of the second premise (knowing the negation of the necessary condition to be true). By identifying the structure of the stimulus, you were then able to correctly parallel that stimulus to the answer choices and choose the correct one. This is what the original post is describing, albeit in a less straightforward way.

Good job!

[AM4747]

Hello,

I have question about positive correlations.

The stimulus says that the older a country, the more likely that it is a monarchy. If this were true, based on this sentence alone, can we infer that the newer a country, the less likely that it is a monarchy? And can we say that if a country is a monarchy, then it is probably old?

In other words, do the rules of mistaken negation and mistaken reversal apply in such cases? Can you please provide the general rules (if any) of inferences from correlative or causal statements?

Thanks
All best

[Adam Tyson]

If we accept a correlation as true, AM4747, then yes, we can make those inferences (as one thing increases, so does the other, and vice versa). Those are not mistaken reversals or mistaken negations, because the correlation is not conditional.

A few examples might help, rather than fixed rules (and keep in mind that these not be factually true in the real world - we are just accepting them as true for our purposes):

1. The larger a mammal gets, the more likely it is to suffer from spinal dislocations

Correct inference: A small mammal is less likely to have spinal dislocations than a large one

Bad inference: This mammal is large, so it probably has spinal dislocations

Why it's bad: "more likely" does not mean "likely". Maybe the odds go from 01% at the low end of the scale (the smallest mammals) up to 3% at the high end (the largest mammals). That would mean that even the largest mammal is still very unlikely to have them (97% do not).

2. If you collect comic books, as your collection gets larger it gets more valuable

Correct inference: Bob's comic book collection is larger now than it was a year ago, so it is more valuable than it was then (again, not necessarily in the real world, as other factors may diminish the value; we are just accepting this claim for our purposes here)

Correct inference: Bob lost a few of his comics, reducing the size of his collection, so it is less valuable than it would have been had he not lost them.

Bad inference: Margo's collection has shrunk in size from where it was 10 years ago, so it is less valuable than it was then.

Why it's bad: We can't go backwards with this correlation, because there may be other factors that contribute to value IN ADDITION to the size of the collection, such as the age of the books. Bigger means more valuable, but smaller may not mean less valuable. Tricky!

Bad Inference: Bob's collection of comics is larger than Margo's, so Bob's collection is more valuable

Why it's bad: The correlation was about a single collection growing in value as it grows in size, and tells us nothing about the comparative values of different collections. Margo may have a few very valuable comics while Bob has a lot of comics that aren't very valuable. As Margo gets more, her value grows, and as Bob gets more, so does his. We cannot compare the values to each other.

So, to your question about the monarchy/age correlation here: it is a good inference that the younger a country is, the less likely it is to be a monarchy. That's relative - less likely than if it was older. However, we cannot infer that if a country is a monarchy it is probably old, because we don't know enough about how many old and young countries there are or what the odds are at each end of the scale. Even if 100% of old countries are monarchies, while only 20% of young ones are, there could be many more young countries than old ones. Of 1000 countries, maybe 900 are young, and 180 of those (20%) are monarchies. The other 100 are old, and they are all monarchies (100% - higher odds, but still a smaller number). With 280 total monarchies, the odds of any one monarchy being old are lower (about 1 in 3, roughly) than the odds that it is young (about 2 in 3). Fun with math!

As to the relationship between correlation and causation, just remember the golden rule here: correlation NEVER proves causation!