One of the reasons that inference questions tend to be so difficult is that most people who take the SAT or ACT have never been exposed to basic formal logic (at least in a non-mathematical context) and consequently have no idea of the rules that the tests are playing by.

While reading is by nature considerably more subjective than math, the basic kinds of reasoning that govern the two sections are far more similar than what most people realize, and nowhere is this more apparent than on inference questions.

It is first of all necessary to distinguish between inference and speculation.

According that all-encompassing source of knowledge, Wikipedia, inference can be defined as “the act of drawing a conclusion by deductive reasoning from given facts.”

Speculation, on the other hand, can be defined as “a conjecture (guess), expressing an opinion based on incomplete evidence.”

Most incorrect answers to inference questions fall into the realm of speculation; that is, they could be true based on the information in the passage, but usually we simply don’t have enough information to judge whether they are actually true. The correct answer is the one that can actually be deduced from the facts presented.

Now, for a given assertion, “If x, then y,” there are two valid inferences: one is the statement itself, and the other is the contrapositive: if not y, then not x.” So, for example, from the statement: “if a creature is a dog, then it is an animal,” we can make the valid inferences that:

1) A creature that is a dog is an animal (rephrasing of the statement)

2) All creatures that are dogs are animals (rephrasing of the statement)

3) if a creature is not an animal, then it is not a dog (contrapositive)

This is the essential basis for inference questions. The tests do not go so far as to deal directly with contrapositives, although using them can help on occasion. Most often, the correct answer to an inference question will quite simply be a rewriting of the of the original statement from a different angle.

For example, if a passage states that the mass of a red dwarf star is smaller than the mass of the sun, the correct answer to an inference question about that fact might be that the mass of a red dwarf star is not larger thanthe mass of the sun. Incorrect answers will simply be outside the bounds of that statement and involve speculation.

They might say things like, “Red dwarves have the smallest mass of any object in the solar system” or “It is more difficult to determine the mass of a red dwarf than it is to determine the mass of the sun.”

The key to dealing with these statements is to make sure that you are absolutely clear about what the statement in question actually says. Take a couple of seconds, make sure you understand it, and write it down in your own words, then look for the answer closest to that statement. It should be correct.