It’s important to be ever-cognizant of the fact that on a multiple choice test, one of the 5 answers has to be right. Because of this, it’s sometimes possible to answer a question correctly by starting at the end, and ending at the start. Most in the prep world call this “backsolving,” and it’s even more powerful on the SAT because the SAT will always put numerical answer choices in order, making it even easier for us to do this efficiently. Pattern recognition, folks: it’s super important.

Anyway, let’s have a look at a backsolve example. The setup for this question comes from a contest winner; I apologize in advance if it’s too macabre (or just plain weird) for you.

  1. Rex is a dinosaur who eats kids who eat nothing but corn. He eats 1/4 of the kids on his island on Monday, 13 kids on Tuesday, and half as many as he ate on Monday on Wednesday. If there are 22 kids left on the island on Thursday, and no kids came to the island or left in a way other than being eaten in that time period, how many kids were on the island before Rex’s rampage?
     
    (A) 56
    (B) 64
    (C) 68
    (D) 74
    (E) 75

Instead of trying to write an equation to solve this, let’s use the fact that one of the 5 answers has to be right to our advantage. If we start with answer (C), we’ll have to try 3 answers in the worst case scenario, since (C) is in the middle and if it’s not right we’ll know right away whether we need to go higher or lower.

I’m going to set up a table to keep track of what’s going on, but when you do this on your test you certainly don’t need to set up a table. You just need to pick an answer choice to start with — almost always (C) — and follow the instructions in the question to see whether everything is internally consistent.

As the table above shows, if (C) is true and 68 kids were on the island before the carnage, then 17 kids were eaten Monday, leaving 51. Then 13 kids were eaten Tuesday, leaving 38. Half of the kids who were eaten Monday were eaten Wednesday, which means on Wednesday Rex only ate 8.5 kids. We know (C) isn’t right if it’s leaving us with a fraction, but more importantly, we know that the number of kids left according to (C), 29.5, is too big. Remember, we’re looking for 22 kids left on the island, so our answer must be smaller than 68. Let’s try 64 instead:

As you can see, 64 doesn’t work either, but we’re getting closer. At this point, we’re pretty confident (A) is our answer, but it also shouldn’t take us very much longer to confirm it:

Alright. Nice. We’ve successfully summarized a gruesome scene with a neat and tidy table. Success!

So how do you know when to try backsolving? In general:

  • If the answer choices are numbers (that go in order — they always will), there’s a good chance you can backsolve.
  • If the question is a word problem, your chances get even better.

Practice, of course, will make this easier and easier. As with any new technique, you’ll want to make sure it’s second nature for you, even on hard questions, before you sit down for the real test. So practice backsolving on hard questions now, and reap the benefits on test day. It’s rare to find a test that doesn’t have at least a few good backsolves on it.

No more dinosaurs eating children (probably)!

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For more tough backsolve problems, try this and also the last question here. For even more, browse the “backsolve” tag on my Tumblr for some recently posted examples!