One of the biggest differences between the SAT and other non-multiple choice tests is that for nearly every question on the SAT, the correct answer is right in front of you! Given that the answer is right there, the real trick is figuring out how to use this to your advantage. Let’s look at an example to show us how we can use these answer choices to our advantage.
“If x and y are numbers such that (x + 11) (y – 11) = 0, what is the smallest possible value of x² + y² ?”
The first thing to recognize is that one of these answers is the correct answer. This means that, given the parameters of the problem, one of these choices should spit out an answer that makes sense if used in the above equations. The easiest thing to do to check which answer choice will give a plausible solution is to plug one of the choices in to our given equations.
x² + y² = 0 (Plausible, both x and y must be 0)
(0 + 11)(0 – 11) = 0 (not possible)
By plugging in our first answer choice we are given some very important information. We see that in the equation “(x + 11) (y – 11) = 0”, one or both of the quantities within the parentheses must be zero. That is one of those rules of algebra that we all learned a million years ago in our first algebra class called the zero- product property : If ab = 0, then a = 0 or b = 0. Given this fact, we need x to equal -11 or y to equal 11 in order for the first equation to be possible. This will help us in testing our next answer choices.
x² + y² = 11 (Not plausible given we need x to equal -11 or y to equal 11)
x² + y² = 22 (Not plausible given we need x to equal -11 or y to equal 11)
x² + y² = 121 (Plausible, x² could equal 0 and y could equal 11, or x could equal -11 and y could equal 0)
(-11 + 11)(0 – 11) = 0 or (0 + 11)(11 – 11) = 0 (Plausible)
At this point we are actually done. The answer choices are always listed in order of smallest to largest and we are looking for the smallest number that would satisfy these parameters. Even if (E) gives us a plausible answer, it is a larger number than (D) and, thus, is an incorrect answer.
There are a number of different kinds of problems where plugging in the answer choices are useful, but these tend to be problems where either an equation or some parameters are given and the goal is to find out which answer choice fits given what is stated in the problem. Even if plugging in an answer choice doesn’t give an immediate answer, it can shed some light onto some aspect of the problem that might not be immediately visible, as we saw above. So go ahead and use those answer choices. They are there to help you – not to hurt you!
David Greenslade is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles here, including How I Scored in the 99th Percentile and How to Effectively Study for the SAT.