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Lucas Fink

SAT Shortcut: Avoid Algebra By Drawing Word Problems

It’s pretty often on the SAT that you’ll have the choice of doing something algebraically or by some other route. While you might be pretty comfortable working with equations, it’s often not so easy to figure out how translate the words on the page into a workable algebra problem. And you might not even have to; sometimes, just figuring out the logic behind a problem is all you need to do. And the best way to do that is to start sketching the situation out.


Why creating equations can be difficult

Carrie invites some friends to a party. For every two friends who bring snacks, there are five who bring nothing with them. If the number of friends who bring nothing is 15 more than the number of friends who contribute snacks, how many friends in total arrive at the party?

We’re missing a couple pieces of information in this question. We don’t know the total number of friends who bring Hot Cheetos and Takis, nor do we know how many of her friends are total bums.  (We do know that Carrie needs to find better friends, though).

But let’s try writing out an equation, if we can.

We’re trying to arrive at the total number of people at the party, which we’ll call g (for guests). That’s the sum of two numbers that have a difference of 15. Lets call those numbers f (friends with Funyuns) and m (moochers).




Hm. So far, nothing’s jumping out. But we do know something else: there are 2 friends with Funyuns for every 5 moochers. That means that 2/7 of the guests, g, have Funyuns, f, and 5/7 of g are moochers, m.

That’s f=2g/7

and m=5g/7

And from here, things are relatively simple. Plug those into our equation for the difference of m and f.





And there’s our answer. But…


Drawing the word problem is faster

If the equation above isn’t totally clear, don’t worry. This problem is about to get easier.

But maybe you got the right answer pretty comfortably with the algebra—and if that’s true, then great—but remember that the SAT is timed, which means that the fastest way is the best way.

By just drawing some of Carrie’s crummy friends, we’ll get there faster.


Alright, so on the actual SAT, you won’t have the luxury of my Microsoft Paint masterpiece. You’ll just draw some circles and squares, or something similar.

It’s pretty clear on seeing this that 2/7 of the friends have snacks and 5/7 don’t. You can also see what the difference is… that’s 3/7. So just do a little mental highlighting and copy-pasting of that picture.




…How many groups of these guys will we need to make the difference be 15? If there are 3 in each group, we’ll need 5 groups. Five groups of seven people total? That’s… 35 total. Right.


Pictures and diagrams help keep you focused on the SAT

It’s a lot easier to stay focused and get your foot in the door of a word problem if you start sketching out the situation like this. Even if you saw the mathematical relationship pretty quickly in this example, there will almost definitely be more difficult problems on the SAT that are best drawn, at least in the beginning. And if the math becomes clear soon after, then great—the picture has served its purpose.


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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