Many times on the SAT, you’ll have the option of putting some concrete numbers into an expression or equation to check what its results look like. When you’re faced with an algebra problem that you’re not totally sure how to tackle, that can be a great strategy. Even if the SAT makers are trying to test your algebra skills, you can change the game and do some number punching on your calculator instead, and that may save you both time and frustration.
But those questions that you can plug numbers into might give you some rules to follow, and you’ll have to make sure the numbers you choose are appropriate.
If the question tells you that x is a prime number, can you try plugging in a 1? If x is an integer, can you choose 0?
Here are some definitions that you’ll need to plug numbers in on your SAT. You probably won’t find these in your SAT vocabulary flashcards…
Integers are all of the counting numbers (1, 2, 3…), their negatives (-1, -2…), and zero. Basically, they’re not fractions or decimals. If you’re told that x is any integer, then, you’re probably going to want to try plugging in a positive number, a negative number, and zero. That is, unless the positive plug-in got you to the right answer—you won’t always have to try more than one number for the variable.
Alternatively, you might also want to try varying between odd and even numbers for your choices, especially if the question mentions either.
Odds and evens
Say the SAT asks which of the expressions in the answer choices always results in an even number. If you have in an answer choice, is it always even? If you put a 1 in for x, it comes out to . And that looks even, right? Nope. Fractions are neither odd nor even; only integers can be.
On the other hand, 0 is even, since it’s an integer that’s neatly divisible by 2. .
Prime number have two and only two factors; they’re divisible by only themselves and 1. So 3 is prime, because no other numbers than 3 and 1 go into 3. So are 5, 7, 11, 13, and an infinite number of other odd numbers.
But there’s one odd man out, so to speak. 2 is prime, even though it’s even, since it has only 2 and 1 as its factors. It’s both the only even prime and the smallest one.
1 is not prime, nor is 0. 1 only has one factor (1) and primes need two. 0 has an infinite number of factors, since anything times zero is zero. And neither fractions nor negatives can be prime. Only whole numbers can be.
If you’re asked to plug in, and it has to be a prime number, try 2 and 3 first. They’re the easiest to work with, and between the two of them they’ll cover most situations.
Factors and multiples
Students occasionally get these two mixed up, although they know generally what they are. Let’s use a simple mnemonic to be sure you don’t do that on your SAT. If I say there are multiple chicken pot pies in my fridge, you think “many.” If I say there are many factors in making a good pot pie, you might think “ingredients.” Remember that multiples are many, and factors are pieces.
So what’s the smallest multiple of 179? No, you don’t have to multiply it. It’s 179. By the same token, what’s the largest factor of 179? Again, it’s 179. Every number is both a factor and multiple of itself, and that’s key for certain SAT word problems. In case you’re wondering, 179 is also prime, so other than 1, it’s the only factor.
Follow the SAT’s rules
Make sure you watch for these words in word problems and keep them in mind when you choose numbers to plug in. First, choose a normal example of the type of number, like a 3 for “an odd integer. ” Then, if your first plug-in doesn’t give you results, plug in one of the strange numbers, such as 2 for a prime, or 0 for an integer. Simply knowing these definitions is one of the easiest ways to improve SAT math.