SAT Guessing Strategy: The Real Deal

My recent post on an article I found about the Princeton Review included a passing remark that the SAT punishes guessing, rather than rewarding it.

This drew a posted comment from one reader, and several emails from other readers, asking for clarification. (By the way–while I welcome all remarks and comments in any form, it’d be great if you’d consider posting comments to the blog directly. That way everybody can benefit from your ideas.)

So I’ve decided to do a series of blog posts on the role of guessing in each of the standardized tests I cover. We’ll start with the SAT today, since that’s the one that got the ball rolling. Look for an article on GRE guessing a week from now, and an article on LSAT guessing a week after that. (I’ll be posting other articles between these ones, of course.)

So let’s get started. My earlier comments on the Princeton Review article already explain the basic guessing advice when it comes to the SAT, which can be boiled down to this:

If you can’t answer a question, use what you know about the question to eliminate as many answer choices as possible, and then guess from the remaining ones.

The idea behind this is that you’ll be guessing from a smaller number of answer choices, which ups your odds of being correct. In theory, following this advice should let you outpace the wrong-answer penalty on the SAT.

(What’s the wrong-answer penalty on the SAT, you ask? On multiple-choice questions, the SAT awards one raw point for every correct answer choice and subtracts one quarter of a raw point for every incorrect answer. They do this so that guessing won’t affect your score. They reason that if you guess randomly from five answer choices, you should be right 20% of the time and wrong 80% of the time. The quarter-point deduction on the wrong answers should counteract the correct guesses.)

This “guessing strategy” on the SAT is the single most popular piece of test-taking advice in history, as far as I can tell. Everybody who preps for the SAT learns this strategy. Every major test prep company teaches it.

And, like so many other things taught by every major test prep company, it doesn’t actually work.

The normal SAT guessing strategy makes two assumptions. First, it assumes that you’re able to eliminate wrong answer choices successfully even when you can’t answer a question. Second, it assumes that you choose randomly from the remaining answer choices.

Unfortunately, the first assumption is very often incorrect–and don’t even get me started on the second assumption :)

These assumptions ignore the way that SAT questions are actually written. Let me give a couple of examples.

Example 1: Both assumptions are valid

Suppose I give you a multiple-choice math question that looks like this:

If x|(yz) = 22, then j|(kl) = :

(a) 15
(b) 26
(c) 38
(d) The Chicago Bears
(e) Bordle

[PLEASE NOTE THAT THIS ISN’T A REAL MATH QUESTION. IT’S DESIGNED TO BE UNINTELLIGIBLE. BEAR WITH ME.]

In this example, since the question is a pure math problem, it’s pretty clear that (d) and (e) can’t be correct, since they aren’t numbers.

It’s equally clear that a student will have no idea what the question is asking (since I made up an operation and didn’t define it).

Given those two conditions, it would be possible for a student to think this way:

I know (d) and (e) must be incorrect, so I can eliminate them. I have no idea what kind of math problem I’m looking at, and all the answers seem equally plausible to me, so I’ll pick (b) for the heck of it and get on to the next question.

This would be a perfect application of the popular guessing strategy: First the student eliminates the obviously incorrect answer choices, and then she picks randomly from what’s left.

Example 2: Only The First Assumption Is Invalid

But SAT questions don’t have answer choices like the ones we just used. Instead, let’s say the answer choices looked like this:

(a) 2.5
(b) 7
(c) 22
(d) 44
(e) 45

With answer choices like these, the student can’t eliminate anything with the same certainty she had when she got rid of (d) and (e) in the first example. Any answer choices she eliminates could conceivably be correct. Let’s say she eliminates (a) and (e) on the theory that she doesn’t like decimals or multiples of 5. (That’s as good a reason as any other, given the circumstances.)

After making these eliminations, the student might go on to pick an answer choice. Since she doesn’t know anything at all about the question, she decides to pick an answer choice at random and chooses (c).

In this example, the first assumption in the guessing strategy fails because the student has no basis for eliminating any of the answer choices. Since the correct answer choice might have been accidentally eliminated from the random guessing process, the chance of guessing correctly is still only 1 in 5, for all the student knows.

On an example question like this, the second assumption in the strategy would still be good–the student’s guess is still random, since she has no knowledge that might influence it.

Example 3: Only The Second Assumption Is Invalid

Now imagine a slightly different prompt with the same answer choices we saw in the first example:

If x|(yz) = 22 and a|(bc) = 23, then j|(kl) = :

(a) 15
(b) 26
(c) 38
(d) The Chicago Bears
(e) Bordle

In this example, (d) and (e) are clearly incorrect, just as they were in the first example. They can be eliminated without hesitation. The first assumption in the guessing strategy has been satisfied.

But what about the second assumption, which requires a student to guess at random from the remaining choices? Imagine that our test-taker notices that both of the example expressions in the prompt have values in the 20’s. Based on this, she decides that (b) is more likely to be correct than the other answer choices, since it also has a value in the 20’s. She marks (b) on her answer sheet and goes on to the the next question. Unfortunately, since her choice was influenced by what she thought she knew about the question, the second assumption of the guessing strategy isn’t met. Our test-taker can’t count on out-pacing the wrong answer penalty if she keeps interfering with the necessary random selection.

Example 4: A real SAT question with neither assumption satisfied

Now let’s take a look at a real SAT question. This one is number 20 from page 400 of the College Board publication The Complete SAT and PSAT Strategy Guide:

The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set?

(a) 25
(b) 26
(c) 50
(d) 51
(e) 52

If you know how to answer this question, it looks relatively straightforward. (By the way–this question only requires you to know the number line, which most students learn in middle school, but it’s still ranked a “hard” question by the College Board, which means a lot of test-takers got this question wrong. Remember that the subject matter on the SAT isn’t difficult–the design is what makes the SAT difficult. But I digress.)

But what if you don’t know how to answer it? After all, it’s only when you don’t know how to answer something that you’d use the guessing strategy anyway.

Here, you can see that none of the answer choices is clearly out of place. If you don’t know anything about how to answer the question, any of the answer choices seems plausible:

• 25 is mentioned in the problem.
• 26 is mentioned in the problem.
• 50 is two times 25.
• 52 is two times 26.
• 51 is right in the middle of 50 and 52.

If you don’t know how to answer the question, how would eliminate answer choices here, and be sure you weren’t eliminating the correct one?

And let’s say you do manage to make a correct elimination, by chance. Now we have to worry about the second assumption of the guessing strategy–guessing randomly from what’s left.

Since you know a little bit about integers (or you should, if you’re taking the SAT), you probably feel that one or two of the answer choices is more likely to be correct, so you pick that one. Notice that this isn’t a random selection. If a random selection is like flipping a coin, then picking the answer choice that seems to have the best chance of being right is like stopping the coin in midair and placing it heads-up: There’s no randomness anymore, and any expectation of your results that’s based on randomness has to go out the window.

So what does a real test-taker do when she uses the “guessing strategy” on a question like number 20 above?

The inner monologue on that thought-process goes something like this:

Okay, I don’t know how to answer this question. But I know what integers are, and I know what “consecutive” means, so let’s give it a shot. I like (b), so I’ll say I don’t think it’s (a) or (d) and eliminate those two. And then my random guess will be (b).

Like I said, there’s nothing random about that selection at all, and there’s no real basis for eliminating (a) and (d), because the student’s understanding of the question isn’t complete.

SAT questions simply aren’t designed in a way that would make the popular “guessing strategy” a good idea.

The result is that the “guessing strategy” gives people a sense of false confidence, causing them to mark answers for questions they should be skipping. At a quarter of a raw point per wrong answer, these guesses add up quickly.

That’s why I say the SAT punishes guessing. If you follow the standard guessing advice on this test, you’ll be wrong way more often than pure probability would suggest. Your score will suffer for it.

Don’t Believe Me?

If this is the first piece of advice you’ve ever gotten from me, by this point you probably think I have no idea what I’m talking about. How can I say something that blatantly contradicts the conventional wisdom of millions of test-takers?

But don’t worry–you don’t have to take my word for it. Let’s look at some other evidence that backs up my idea that guessing on the SAT is a bad thing.

First, you don’t know anybody who’s guessed their way to a top score. I promise you that. Without exception, every top-scoring (99th percentile) test-taker I’ve ever asked about it has told me that they didn’t guess. If they came to a question and they weren’t sure of the answer, they left the question blank. If the guessing strategy were as effective as people would like you to believe, there should be a significant number of people guessing their way into top scores. And there isn’t.

Second, the College Board knows about the “guessing strategy,” and it hasn’t changed the SAT in response. We know they know about it because the “guessing strategy” is in their book, on page 15. (Don’t go thinking that it must be good advice if it comes from the College Board. Most of the test-taking advice in their book is useless, like the essay-scoring rubric on page 105 that the essay graders ignore.) In 2005, the College Board carried out a major overhaul of the SAT - but they left the wrong-answer penalty intact. Now ask yourself this: If the College Board knew about the guessing strategy, and thought it worked, wouldn’t they expect students who used it to get higher scores? And since the College Board is always doing everything it can to make the test less “coachable,” wouldn’t they take the opportunity to remove the wrong-answer penalty in an effort to level the playing field for test-takers? Of course they would . . . if they thought the “guessing strategy” helped people.

So . . . What Should You Do Instead?

The next question, of course, is what you should do instead of guessing.

The key is to develop a high level of familiarity with the test so that you can know when you’re about to be wrong, and you can know how to answer more questions by relying on the test’s design.

That might sound crazy, but trust me on this: The SAT is designed according to certain rules and patterns, as I always say. Those rules and patterns are easy to learn, but–for whatever reason–most test prep resources just don’t share them with you.

When you learn these rules and patterns and practice applying them, you develop a sense of when you’re right. You feel it with certainty. And you can also feel when this certainty isn’t present. In other words, you can feel the difference between a question you know you’re about to answer correctly and a question you know you’re about to guess on.

Most importantly, you’ll also be able to start answering more questions correctly, because you’ll understand how they’re designed and how to take them apart.

So the first step in the process is to stop guessing. Stop treating the SAT like it’s a haze of right and wrong answers that may or may not be correct depending on interpretation. Start realizing that every question has one correct answer choice. And don’t mark answers that you aren’t sure of.

Would you like to learn more about taking the SAT? Please check out my free white paper and the sample chapters from my SAT Guide. Then, if you’d like to order a copy of the Guide, go to this link.