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Lucas Fink

SAT Math Problems Are Puzzles

You know how the SAT doesn’t go into high-level math? That’s because SAT math isn’t really about what you learn in math class. Since the SAT is supposed to be for students going into any type of college program, the math section is actually built around how well you can solve puzzles, in a way. Sure, there are formulas at play, but at its heart, the SAT cares less about formulas than it does about logic. This is one of the most common mistakes students make while studying for the SAT.


You’re biologically programmed to enjoy logic

There’s something about the human brain that loves a challenge. It’s not hard to find examples of it if you look around. We’ve only made the kinds of scientific progress that we have because we’re always trying to figure stuff out. Electricity, engines, agriculture… almost everything around you exists because somebody at some time started screwing around, looking at how things work and how they could use that to their advantage.

And then there’s puzzles. I don’t mean jigsaw puzzles—although those can be nauseatingly difficult—but logic puzzles. Sudoku is a perfect example because it exists only for the joy of doing it. After you finish one, your reward is a square of numbers. Thrilling.

Yeah, it varies from person to person. But at the most basic level, that’s part of what makes us human (and why it’s so strange to see a bird solve a puzzle). If you take away the negative associations—i.e. school—and the pressure, there’s something inherently satisfying and enjoyable about logic problems.


SAT math is logic

The SAT takes relatively basic principles of algebra and geometry and uses them in interesting ways. Even if you know all the rules, any questions past the easiest in a math section are going to require something else. They take the same thing it took for that bird to work out how to use the wire: reasoning. That’s why the official name is the “SAT Reasoning Test.”

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Here’s an example:

If the sum of the consecutive odd integers from x to 11, inclusive, is -45, what is the value of x?

(A) -56

(B) -34

(C) -21

(D) -17

(E) -13

Now, you could do a couple of things here. You could try to work out an equation (good luck with that). You could plug in answer choices and eliminate, but that might take a really long time. Try it with (C) and you’ll see what I mean.

What you really want to do—and what the SAT wants you to do—is to start exploring. It’s a puzzle, and your goal is to find the trick to it.

You know x is less than 11 by the phrasing, so just think about what happens when you add the odd numbers less than 11. The sum gets bigger and bigger (11+9+7+5…), at least at first. But then you might notice the negative number in the question. What does that mean?

At some point, working down from 11, you’ll get into negatives, and they’ll start cancelling out the positives.

And there’s the key that the question is built around. The negatives cancel out the positives, which means you’ll get to a sum of 0 when you add all the odd numbers from -11 to 11. Once you see that, it’s almost too easy. Add the next consecutive odd integers until you get to -45.

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That’s (-13) + (-15) + (-17) = -45

No formulas, no intense calculator work.


Enjoy yourself while you prep

With all that in mind, go into your SAT practice problems with a more positive mindset. It’s not busy work, and it’s not about memorizing. It’s a puzzle. And if you need more structured prep, then check out the 1 Month SAT Study Schedule.


About Lucas Fink

Lucas is the teacher behind Magoosh TOEFL. He’s been teaching TOEFL preparation and more general English since 2009, and the SAT since 2008. Between his time at Bard College and teaching abroad, he has studied Japanese, Czech, and Korean. None of them come in handy, nowadays.

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