Logical reasoning PrepTest 158 · Section 3 · Question 14

This answer choice features a "some" premise, a conditional premise, and a "some" conclusion ("not ... all" can be translated to "some do not"). However, the non-negated term in the conclusion ("biology") is not the sufficient condition of the conditional premise ("kindergarten teacher"). This makes this argument structurally dissimilar to the passage, which means it does not commit the same flaw. An experienced test-taker might eliminate this answer choice without diagramming.

If you wanted to diagram, either as practice or to make sure, we could diagram this answer choice as:

1. High School Teacher -some- Biology
2. Kindergarten Teacher → NOT Biology

Conclusion: Teachers -some- NOT Biology

(Note that "not ... all" is best translated to "some do not," so this conclusion can be read and diagrammed as "some teachers do not teach biology.")

This argument is valid. If kindergarten teachers do not teach biology, it must be true that some teachers do not teach biology. Since this argument is not even flawed, it is incorrect.

This answer choice features a "most" premise. The argument in the passage did not feature a "most" statement at all, so this answer choice should be eliminated immediately. Obviously, this answer choice cannot make an invalid combination of a "some" premise and a conditional premise if the answer choice does not feature a "some" premise.

If you wanted to diagram, either as practice or to make sure, we could diagram this answer choice as:

1. School Board Member -most- Teacher
2. Teacher → NOT Prefer Admin Work

Conclusion: School Board Member -most- NOT Prefer Admin Work

(Note that "few" is best translated to "most do not," so this conclusion can be read and diagrammed as "most school board members do not prefer administrative work to teaching.")

This argument is valid. To validly combine a "most" and a conditional statement, the term shared by both must be the sufficient condition of the conditional statement. When the term shared by both is the "necessary" condition of the "most" statement, we can draw a "most" conclusion with the non-shared terms. Since both criteria are satisfied in the above case, we can validly draw the conclusion that most school board members do not prefer administrative work to teaching. Since this argument is not even flawed, it is incorrect.

Argument or Facts:
Argument

Valid or Flawed:
Flawed

Question Type:
Flawed Parallel Reasoning

Stimulus Summary:
Some freelancers sell work to lax magazines. But a self-respecting writer wouldn't sell their work to a lax magazine. Therefore, some self-respecting writers are not freelancers.

Strategy Overview:

1. Argument or facts? Always argument, so identify premises and conclusions of argument
2. Diagrammable?
   1. If yes, diagram out premises and conclusion.
   2. Note key identifiable characteristics of argument (How many premises? Quantifiers? Ands/ors? Didn't reverse or negate?). Can also convert specific terms in diagram to As, Bs, Cs, Ds, etc.
      1. Eliminate an answer choice as soon as you notice it doesn't possess a key identifiable characteristic the passage possesses
      2. Diagram remaining until you find a matching flaw
   3. If not, paraphrase what the flaw is
      1. Checking to see if a common logical fallacies is committed is very helpful
      2. Select answer choice that has the same flaw

Answer Anticipation:
This argument features quantifier keywords ("some," twice) and a conditional keyword ("No"), which is a strong signal we should diagram the premises and conclusion. We'll diagram the first premise and conclusion (the latter is clearly marked with a "Therefore") as "some" statements. And we'll remember to cross off the necessary condition of the second premise, as that is a "No" statement. Our diagram should be:

1. Freelance -some- Lax Magazines
2. Self-Respecting Writer → NOT Lax Magazine

Conclusion: Self-Respecting -some- NOT Freelance

Since this is a Flawed Parallel Reasoning question, it shouldn't surprise us that this is an invalid combination of a "some" statement and a conditional statement. If we take the contrapositive of the second statement (Lax Magazine → NOT Self-Respecting Writer), we can more easily see what a valid combination would look like. Remember the rule of combining a "some" statement and a conditional statement: (1) the term shared by the two statements must be the sufficient condition in the conditional statement, and (2) the conclusion must be a "some" statement containing the two non-shared terms. Because the first rule is satisfied, we validly could conclude:

Freelancer -some- NOT Self-Respecting Writer

However, the stated conclusion (Self-Respecting -some- NOT Freelance) reverses and negates both conditions. Although "some" statements are reversible, we cannot validly negate both conditions (in other words, we cannot validly take the "contrapositive" of a "some" statement).

Experienced test-takers, working under time pressure, can also use some of the key characteristics of the argument to eliminate certain answer choices without diagramming. Most glaringly, the correct answer will need a "some" premise, a conditional premise, and a "some" conclusion. An answer choice that does not feature these three propositions can be eliminated without diagramming. An even more experienced test-taker could further note that the non-negated term in the conclusion (in the passage, "self-respecting writer") will need to be the sufficient condition of the conditional premise.

Answer Choice Explanation:
This answer choice features a "some" premise, a conditional premise, and a "some" conclusion ("not ... all" can be translated to "some do not"). Moreover, the non-negated term in the conclusion ("members of the Calculus Club") is the sufficient condition of the conditional premise. This makes this argument structurally similar to the passage. An experienced test-taker might, after confirming that the rest of the choices are structurally dissimilar to the passage, elect to select this answer choice without diagramming.

If you wanted to diagram, either as practice or to make sure, we could diagram this answer choice as:

1. Students -some- Prefer History
2. Calculus Club → NOT Prefer History

Conclusion: Calculus Club -some- NOT Students

This is an invalid combination of a "some" statement and a conditional statement. Importantly, it's invalid for the same reason as the argument in the passage. If we take the contrapositive of the second statement (Prefer History → NOT Calculus Club), we can more easily see what a valid combination would look like. Remember the rule of combining a "some" statement and a conditional statement: the term shared by the two statements must be the sufficient condition in the conditional statement; (2) the conclusion must be a "some" statement containing the two non-shared terms. Because the first rule is satisfied, we validly could conclude:

Students -some- NOT Calculus Club

However, the stated conclusion (Calculus Club -some- NOT Students) reverses and negates both conditions. Although "some" statements are reversible, we cannot validly negate both conditions — in other words, we cannot validly take the "contrapositive" of a "some" statement. The flawed conclusion in the passage also appeared to be the "contrapositive" of a properly drawn conclusion. So this answer choice is flawed for the same reason as the argument in the passage.

Key Takeaway:
Experienced test-takers identify characteristics of the argument to save time on diagrammable Parallel Reasoning and Flawed Parallel Reasoning. These key characteristics include the strength of language ("some,' "most," etc.), the number of premises, the presence and location of "ands" and "ors," and the location of certain conditions. A test taker using this technique could eliminate every incorrect answer choice on this argument without diagramming.

This answer choice features a "some" premise, a conditional premise, and a "some" conclusion. However, the non-negated term in the conclusion ("principles") is not the sufficient condition of the conditional premise ("adviser to the debate team"). This makes this argument structurally dissimilar to the passage, which means it does not commit the same flaw. An experienced test-taker might eliminate this answer choice without diagramming.

If you wanted to diagram, either as practice or to make sure, we could diagram this answer choice as:

1. Principles -some- Disciplinarian
2. Adviser to the Debate Team → NOT Disciplinarian

Conclusion: Principles -some- NOT Advisers to the Debate Team

This argument is valid. If we take the contrapositive of the second premise ("Disciplinarian → NOT Adviser to the Debate Team"), we can more easily see why this argument is valid. Remember the rule of combining a "some" statement and a conditional statement: the term shared by the two statements must be the sufficient condition in the conditional statement; (2) the conclusion must be a "some" statement containing the two non-shared terms. Because the first rule is satisfied, we validly could conclude:

Principles -some- NOT Advisers to the Debate Team

Since this argument is not even flawed, it is incorrect.

This answer choice features a "some" premise, a conditional premise, and a "some" conclusion. However, the non-negated term in the conclusion ("popular teachers") is not the sufficient condition of the conditional premise ("coach"). This makes this argument structurally dissimilar to the passage, which means it does not commit the same flaw. An experienced test-taker might eliminate this answer choice without diagramming.

If you wanted to diagram, either as practice or to make sure, we could diagram this answer choice as:

1. Let Students Leave -some- Popular
2. Coach → NOT Let Students Leave

Conclusion: Popular -some- NOT Coach

This argument is invalid, as it equivocates between "leaving early" and "leaving before three o'clock". Otherwise, however, it's a valid combination of a "some" statement and a conditional statement. Ignoring that equivocation, if we take the contrapositive of the second premise ("Let Students Leave → NOT Coach"), we can more easily see what a valid combination would look like. Remember the rule of combining a "some" statement and a conditional statement: the term shared by the two statements must be the sufficient condition in the conditional statement; (2) the conclusion must be a "some" statement containing the two non-shared terms. Because the first rule is satisfied, we validly could conclude:

Popular -some- NOT Coach

Since this argument is not even flawed, it is incorrect.