I’m getting a bit tired of all the focus on #20, which is usually the hardest math question on the test. I guess I’m a bit complicit in all the hype, since I like to illustrate techniques on here using difficult problems, but that’s only because I like to show how powerful those techniques can be. Seriously, let’s be very clear about this: #20 is the LEAST important question on the test. You shouldn’t be worrying about it at all unless you’re getting 780’s or higher every time.  Here’s an argument based on a simple economic principle.

If you’ve taken or are taking an economics course, you’re surely familiar with the concept of opportunity cost. Put succinctly, opportunity cost is the cost of a certain decision in terms of the best available alternative. For example, if you choose to go to the movies (which costs you $10), but if there weren’t any good movies you you would have spent those two hours babysitting for $15/hour, then your opportunity cost for going to the movies is what you paid plus what you COULD HAVE made instead ($40). That’s an expensive movie, right?

Of course, opportunity cost is really just a way to codify the thought processes we have about the decisions we make: “if I didn’t do thing 1, I could have done thing 2 instead; the benefits of doing thing 1 are valuable enough to me that I will forgo the benefits of doing thing 2.” With that in mind, let’s look at some facts about the SAT math section:

Facts:

  • Every multiple choice question is worth the same: +1 raw score point for a correct answer, -1/4 raw score point for an incorrect answer, +0 for a blank.
  • Although they’re worth the same, questions vary greatly in difficulty.
  • You have a limited amount of time to complete a section.
  • In math sections, questions proceed in an order (roughly) from easiest to hardest*.
So here’s the argument:
  1. Since the payoff for a correct response is exactly the same in raw score points no matter the difficulty, and since that’s the only thing that determines your final math score, the value of each question is exactly the same.
  2. Since you can’t really be doing anything else during the 25 minutes in which you’re sitting there taking a 20 question math section, the opportunity cost for working on (and answering correctly) any given question is equal to the time it takes you to answer that question (time that you could otherwise be spending answering the next question correctly).
  3. Since it takes longer to answer hard questions correctly than it does to answer easy questions correctly, questions on the math section have increasing opportunity cost (that is, they take longer) as you progress, even though their values are exactly the same.
  4. Since your mission is to maximize your score (by maximizing the amount of raw score points you secure) in a limited amount of time, the most important raw score points to collect are the ones with the lowest opportunity cost associated with them.
  5. Conversely, mistakes on easy questions are the most costly mistakes, since it would have taken so little extra time to get those questions right.
  6. If #20 is the hardest question in the section (this is usually, but not always true), then it has the highest opportunity cost, and is therefore the least important to get right.
  7. If it’s the least important question to get right, it’s also the least important question to attempt.

You should, therefore, be as positive as possible that you are correct in your response to every question you work on before moving on to the next question (which will have a higher opportunity cost for the same amount of raw score points). You should not even attempt #20 until you are sure you are correct on #19, which you shouldn’t even attempt until you’re sure you’re correct on #18, etc.

I’ve said it before but it bears repeating here: You’ll increase your score more by getting fewer easy questions wrong than you will by getting more hard ones right.

* In the section that has the grid-in questions, questions go from easiest to hardest twice, once in the multiple choice (#’s 1-8) and then again in the grid-ins (#’s 9-18).