OK, so you know how I’m always saying that the SAT is not a math test? This is one of the primary reasons why. On the SAT, it’s often completely unnecessary to do the math that’s been so carefully laid out before you. A lot of the time (and on a lot of the most otherwise onerous problems), all you need to do is make up numbers.
Sounds crazy, right? Well it’s not. It would be crazy to just make up numbers on just about any other pain-in-the-ass task (for instance, it would be bad just to make up numbers on your taxes), but you’ll be dumbstruck by how often it works on the SAT. Of course, you have to practice doing it to get good at it, so that when an opportunity to do it on the real test pops up, you don’t panic and blow it. That’s what your old buddy Mike is here for.
I’m thinking we should start with a more obvious plug-in. If you would consider trying to solve this one with pure algebra, you’re probably out of your mind. Still, it’s a great illustration of the technique:
- If m and n are divided by 8, the remainders are 3 and 5, respectively. What is the remainder when mn is divided by 8?
What we want to do with a question like this is plug in values for m and n so that we’re not dealing with abstracts. Of course, there are infinite possibilities for the values of both m and n, but we’re just going to pick values and stick with them.
Since the problem stipulates that m divided by 8 gives me a remainder of 3, and n divided by 8 gives me a remainder of 5, let’s pick m = 11 and n = 13 (because 8 + 3 = 11, and 8 + 5 = 13). That will keep our numbers nice and low, and make the division we’ll have to do in the next step less arduous.
Since I’ve plugged in 11 for m and 13 for n, I need to find the remainder when 11×13=143 is divided by 8. Remember long division? That’s going to be the easiest way to calculate a remainder, so let’s do it:
Bam. Remainder 7. That’s choice (E). I feel so alive right now.
Note that if we picked different numbers for m and n (like, say, 83 and 85), we’d still get the same answer (try it yourself to see). That’s the beautiful thing about plugging in!
Let’s do another, slightly tougher one:
- If the inequality above is true for integer constant k > 1, which of the following could be a value of x?
(A) k – 3
(B) k – 1
(D) 3k – 4
(E) 3k – 2
OK. Forget for a minute that this can be solved with algebra and think about how to solve it by plugging in. Remember, if you don’t practice plugging in on problems you know how to do otherwise, you won’t be able to plug in well when you come to a problem you don’t know how to solve otherwise!
We know k is a positive integer greater than 1, so let’s say it’s 2. If k = 2, then we can do a little manipulation to see that x has to be greater than or equal to 3:
So, which answer choice, given our plugged in value of k = 2, gives us a number greater than or equal to 3 for x?
(A) k – 3 = 2 – 3 = -1 (too low!)
(B) k – 1 = 2 – 1 = 1 (nuh-uh)
(C) k = 2 (nope)
(D) 3k – 4 = 6 – 4 = 2 (still no good)
(E) 3k – 2 = 6 – 2 = 4 (yes!)
Rock. On. Note again that if we had picked a different number for k, we still would have been OK. Try running through this with k = 10 to see for yourself.
So…when do you plug in?
- When you see variables in the question and the answer, you might want to try plugging in.
- On percent questions, you’ll probably benefit from plugging in (and using 100 as your starting value).
- On triangle questions where no angles are given, you might try plugging in 60 for all angles.
- If you’re plugging in on a geometry question, just make sure that all the angles in your triangles and straight lines add up to 180°.
- Anytime you don’t know something that you think it would be helpful to know, try making it up!
Anything else I should know?
- As a general rule, DO NOT plug in 0 because when you multiply things by 0, you always get 0, and when you add 0 to anything, it stays the same. Usually, that will make too many answer choices work.
- Similarly, DO NOT plug in 1, since when you multiply things by 1, they don’t change. This will also often make more than one choice seem correct.
- DO try to keep your numbers small. There’s no need to plug in 2545 when 2 will do.
- DO think for a minute before picking your numbers. Will the numbers you’re choosing result in messy fractions or negative numbers? We plug in to make our lives easier, so practice avoiding these scenarios!
- You always have to check every single choice when there are variables in the answers and you plugged in, because there’s a small chance that more than one answer will work. If that happens, don’t panic…just try new numbers. You can greatly mitigate this by following rules #1 and 2 above.
Let’s try some more problems!
Note: all of these problems can be solved without plugging in, but you’re not here to do that right now, you’re here to practice plugging in. Don’t be intractable in your methods. If you’re amenable to change, it’s more feasible that you’ll improve your scores.
Want to see more plugging in? Browse the “plug in” tag on my Tumblr for some recently posted examples!