Advanced Guide on Sufficient Assumption Questions

Intro to Sufficient Assumption (Advanced)

This is a continuation of the Simple Guide on Sufficient Assumption Questions. Please familiarize yourself with the concepts discussed there before moving on. This guide is dedicated to identifying and avoiding the pitfalls students run into in the hardest Sufficient Assumption (SA) questions.

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‍Table of Contents:

• Traits of Difficult SA Questions
• Information Overload
• Correct Answer Hinges on Contrapositive Understanding
• Explicit Strengtheners vs Subtle Sufficient Assumptions
• Answer Choices You Are Conditioned to Skip

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Traits of Difficult SA Questions

Test-writers can make these questions more difficult in a few primary ways. One’s ability to do well on these questions generally reflects their proficiency with conditional logic. Test-writers usually make SA questions “curve breakers” by making conditional logic chains harder to follow. This is the most important skill to master, but there are also some less common traps that you should be aware of.

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Information Overload

There are sometimes too many conditional relationships to keep track of. Some SA questions are just a bunch of conditionals in sentence form, and every Answer Choice (AC) is just a link of one variable to another. These feel more like a math problem, and students often consider them the most difficult SA questions. Look at PT 130 S1 Q25.

• Repetition is the best way to improve this skill. You need to try out different techniques to see what works best for you. Diagramming is the main one; if you find yourself unable to keep track of everything by the end of the stimulus, more might be useful. If you look at the variables you wrote down and end up overwhelmed going back to the stimulus, try less (or changing your technique).
• Translating premises in the stimulus into short conditionals in your head is another thing to practice. Our working memory limits what we can hold in our heads, so we need to simplify. When the test-writers flex their scientific jargon, I barely read it and immediately translate it into a letter or word. In general, take a second after a sentence to simplify it to a 1-word per variable conditional relationship.
  
  • For example: “If plastid division fails in chlorarachniophytes, then karyokinesis is impaired.”
    
    • I am mentally translating this to “no Div in C → bad Kar”. This is not precise, but all you usually need is to match the terms when they reappear in the stimulus.

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Correct Answer Hinges on Contrapositive Understanding

Many people know what a contrapositive is, as in they could define it and write that from p → q we know ~q → ~p, and to switch “and” with “or” & vice versa. However, being aware of it is not sufficient to avoid mistakes related to it. I have had many students in the 170+ range who frequently have “false positives” in thinking they identified a contrapositive of the correct answer.

• More commonly, people get questions wrong due to not recognizing them. The more questions you do, the more instinctively you will see them. PT 119 S2 Q23 is one of my favorite questions. While you read conditional statements, consider if the contrapositive would result in a “link” to trigger other variables (that the original statement did not yield). Pay extra attention to negated variables.
• To identify a gap, we should link every variable together and see what remains. Take the following:
  
  • “Every time he goes to McDonald’s, John gets one drink—a soda—and one entree. If John did not drink water, he ate ketchup. Therefore, if John did not eat ketchup, he must not have gone to a restaurant.”
    
    • I will use “Not” here for universal understanding. It is often visually easier to cross out the negated variable. People also commonly use ~ or /, do whatever you are familiar with.

Translated:

P1. McDonald’s→exactly 1 drink (a soda) & entree

P2. Not water→ketchup

C. Not ketchup→Not restaurant

• What is missing to guarantee the conclusion? Right now, our variables seem difficult to link together. Starting from the sufficient variable of the conclusion, what do we know?
  
  • If Not ketchup, we know John drank water (because of the contrapositive of P2). If John drank water, we know he did not get a soda at McDonald’s—as he gets exactly 1 drink—so John must not have gone to McDonald’s (the contrapositive of P1).
    
    • Thus, we know that if Not ketchup→ Not McDonald’s. A sufficient assumption could be “if John goes to a restaurant, he goes to McDonald’s”. The contrapositive would be “Not McDonald’s → Not restaurant,” guaranteeing our conclusion.

Linking contrapositives in the premises is a crucial skill for sufficient assumption questions, as is noticing them in ACs. This skill, along with managing “information overload”, enables us to identify gaps in a conditional chain of logic.

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Explicit Strengtheners vs Subtle Sufficient Assumptions

First, try your hand at PT 115 S4 Q17. Our data currently indicates that 48% of students chose the wrong AC, with only 41% getting it right.

One common mistake I see on the hardest SA questions is ignoring the correct AC because a strengthening AC matches their intuition better than the correct AC, often due to being more specific or explicit in wording. People know the right answer needs to guarantee the conclusion, but still fall victim to cognitive biases when the correct AC is worded in a less intuitively appealing way.

An analogy is the tendency to subconsciously ignore red flags if a prospective romantic partner seems perfect on the outside. An AC could match the gist of your prephrase, but if it is not strong enough to ensure the conclusion is true, keep looking.

The practical advice here is to double-check your intuition when an AC seems almost perfect, but you do not quite see how it brute-forces our conclusion. Flag these questions. You either missed how it guarantees the conclusion or need to go look for the correct AC that you overlooked.

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Answer Choices You Are Conditioned to Skip

I will briefly cover a few sneaky (correct) AC “types” that I see people skip, particularly those who like a formulaic approach (nothing wrong with that). The “traditional” AC structure is simply if (P)→(C).

These questions are not conceptually difficult. However, our data shows students frequently answer these questions incorrectly. “Pre-phrasing”, while not a bad idea, can make one more prone to falling for these tricks. I am not suggesting that these kinds of ACs are frequently correct; the actionable advice is below.

1. Outside Info: The Correct AC Appears Irrelevant
   
   • When making our first pass through the ACs in SA questions, we often have in mind the premises/conclusions and the gap between them. This can lead to ignoring ACs that have outside information that doesn’t match what was in our head. All that matters is what happens when you plug the AC back in and check if the conclusion can be false (or it is guaranteed to be true). Students often skip or cross out ACs with outside information on the first pass.
   • It is true that, usually, skipping an AC when our instinct is “...no way that could be right” saves time. The actionable advice here (specific to SA questions) is that if you are not sure that your selection absolutely guarantees the conclusion, flag it & go back to double-check the other ACs. I have seen students do this and then debate between two incorrect ACs, never considering the correct one due to perceived irrelevancy. Check out PT 151 S2 Q21.
2. Redundancy: The Correct AC Appears Redundant
   
   • There is an important distinction to note here, and it would be frustrating if you missed it on test day. An AC simply paraphrasing something in the stimulus can not be correct—nothing new. Test-writers know that we know this and keep us on our toes.
   • Some correct ACs appear to merely paraphrase a premise from the stimulus. However, the premise was mentioned as part of a conditional relationship but not confirmed to be true. An AC confirming its truth may be sufficient to guarantee the conclusion. Note PT 117 S2 Q13.

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