Self-paced
Support Jack's dog howls whenever a train goes by. ████████████ █ █████ ████ ██ █████ ████ ██ ███████ ███ ████ ██ ██████ ███ ████ █████████ ████ █████ ██ ██ ███████ ███
First: Core Skills
This question hinges on a short list of formal logic skills. Let’s lay them out on the table right now.
1: Whenever indicates a sufficient condition.
In every single answer choice, Premise 1 is worded in a simple “[All/Most/Some] Serious joggers can benefit from good running shoes” structure. Serious joggers comes first in both the sentence and the diagram.
Serious → Benefit
In the stimulus, Premise 1 is worded in the opposite way: “Jack’s dog howls whenever a train goes by.” Howls comes first, but it’s second in the diagram because the word “whenever” indicates a sufficient condition regardless of where in the sentence it appears.
Train → Howls
So Premise 1 looks different than its counterparts in the answer choices, but logically it matches up (except in (B) and (D), which are a “most” and a “some” claim, respectively).
2: “Some” claims are reversible.
The nature of the “some” relationship allows us to swap the terms around and retain its meaning: if some cats are pets, some pets are cats
Cats ←some→ Pets
Pets ←some→ Cats
Recognizing you can flip the wording of “some” claims is also critical to success in this question.
3: There’s only one way to draw an inference from a “some” claim
If you’re rusty on your valid formal arguments, now’s a great time to review. The only valid way to derive an inference from a “some” claim is to put some before all.
Pets ←some→ Cats → Conniving
validly gives you…
Pets ←some→ Conniving
Nothing else works.
Distilling The Argument’s Structure
Get ready to use all those skills, baby! Let’s diagram the argument. Here’s how it looks on a first translation from the English:
Premise 1 : Train → Howls
Premise 2 : Train ←some→ Wash
________
Conclusion : Wash ←some→ Howls
This argument works by putting some before all, but you have to make a few adjustments to see it clearly. Let’s swap the order of Premise 2’s terms and put it first:
Premise 2: Wash ←some→ Train
Premise 1: Train → Howls
________
Conclusion: Wash ←some→ Howls
There we go. If you like a nice pretty chain, it’s easy to make now:
Premise 1+2: Wash ←some→ Train → Howls
Our correct answer choice needs be a valid argument that puts some before all.
18.
The pattern of reasoning in █████ ███ ██ ███ █████████ █████████ ██ ████ ███████ ██ ████ ██ ███ ████████ ██████
a
Every serious jogger ███ ███████ ████ ████ ███████ ██████ ███ █████ ████ ██ █ ███ ███████ ███████ ███ ██████ ██ ███ ██ ████████ █████████ █████ ████ ██████ ███ ███ ███████ ████ ████ ███████ █████ ██████ ██ ███ ██ ████████ █████████
(A) does a lot to mirror the wording of our stimulus, but it subtly swaps Premise 2 and the Conclusion.
(A) starts off by giving us an “all” claim, just like our stimulus. So far so good.
P1: Serious → Benefit
You might think (A)’s second sentence looks pretty good too. It links P1’s sufficient condition to a new concept, which is exactly what Premise 2 in our stimulus does.
P2?: Serious ←some→ Ordinary
But (A)’s second sentence isn’t a premise – it’s the conclusion. (A)’s actual diagram looks like this:
P1: Serious → Benefit
P2: Ordinary ←some→ Benefit
________
Con: Serious ←some→ Ordinary
This diagram asks us to put all before some:
P1+P2: Serious → Benefit ←some→ Ordinary
b
Most serious joggers ███ ███████ ████ ████ ███████ ██████ ███ ████ ███████ ███████ ██████ ██ ███ ██ ████████ █████████ ██ ████ ██████ ███ ██████ ██ ███ ██ ████████ ████████ ███ ███████ ████ ████ ███████ ██████
(B) starts with a “most” claim BOOO GET OUT OF HERE (B) BOOO!!!
Here’s (B)’s diagram:
P1: Serious –most→ Benefit
P2: Serious ←some→ Ordinary
________
Con: Ordinary ←some→ Benefit
If putting some before most were a thing, (B) would… still be wrong because most =/= all.
c
Any serious jogger ███ ███████ ████ ████ ███████ ██████ ███ █ ███ ███████ ███████ ██████ ██ ███ ██ ████████ █████████ ██ ████ ██████ ███ ███ ███████ ████ ████ ███████ █████ ██████ ██ ███ ██ ████████ █████████
(C)’s premises and conclusion are conveniently presented in the same order as our stimulus. They didn’t have to do that – very sweet of them.
As mentioned, the terms in Premise 1 are presented in the opposite order between the stimulus and (C), but that doesn’t matter because they’re logically equivalent. Here’s (C)’s diagram:
P1: Serious → Benefit
P2: Serious ←some→ Ordinary
________
Con: Benefit ←some→ Ordinary
Let’s reverse Premise 2 and put it first, just like we did for the stimulus:
P2: Ordinary ←some→ Serious
P1: Serious → Benefit
________
Con: Benefit ←some→ Ordinary
Wonderful, we’ve put some before all. Look at the pretty chain:
P1+P2: Ordinary ←some→ Serious → Benefit
d
At least some ███████ ███████ ███ ███████ ████ ████ ███████ ██████ ███ █████ ███ ███████ ███████ ███ ██████ ██ ███ ██ ████████ █████████ ██ ████ ██████ ███ ██████ ██ ███ ██ ████████ ████████ ███ ███████ ████ ████ ███████ ██████
(D) starts with a “some” claim BOOO GET OUT OF HERE wait a sec it might just be that (D) is presenting the premises and conclusion in a different order. Let’s look at the other sentences.
TWO MORE “SOME” CLAIMS?!? BOOO GET OUT OF HERE (D) BOOO!!!
Here’s (D)’s diagram:
P1: Serious ←some→ Benefit
P2: Serious ←some→ Ordinary
________
Con: Ordinary ←some→ Benefit
You can’t put some before some that is no good at all.
e
Any serious jogger ███ ███████ ████ ████ ███████ ██████ ███ ████ ███████ ███████ ████████████ ██████ ██ ███ ██ ████████ █████████ ██ ██████ ███ ███ ███████ ████ ████ ███████ █████ ████████████ ███████ ██ ███ ██ ████████ █████████
(E) combines an “all” claim with a “some” claim to derive an “all” claim conclusion. It’s otherwise a good match.
(E) starts off by giving us an “all” claim, just like our stimulus. So far so good.
P1: Serious → Benefit
It then presents a “some” claim linking P1’s sufficient condition to a new concept, which is exactly what Premise 2 in our stimulus does. Unlike answer choice (A), this claim is also a Premise. So far so good, then.
P2: Serious ←some→ Ordinary
The problem comes in the conclusion: “anyone who can benefit from…” and (E) is dead. Here’s the full diagram:
P1: Serious → Benefit
P2: Serious ←some→ Ordinary
________
Con: Benefit → Ordinary