Multiple-Choice Questions
17.1 Multiple-Choice Questions
17.2 Grid-Ins
Multiple-Choice Questions
MC stands for all kinds of things. Rappers. Motorcycles. Master of ceremonies. Even Mariah Carey. On the new SAT, MC means good old multiple-choice questions: a question, maybe a graph or a geometric figure, and then five answer choices. About 70 percent of the entire SAT Math consists of these little babies. Know how to handle ’em, and you’ll be crushing every MC on the block come test day.
For every math multiple-choice question on the test, you have two options:
  • Solve the problem directly.
  • Use the process of elimination.
In general, solving the problem is faster than going through the answer choices using process of elimination. Also, in general, if you’re at all uncomfortable with the topic, it can be beneficial to try to eliminate answers instead of just solving the question.
Solving the Problem
Solving a problem directly is pretty straightforward as long as you feel comfortable with the math being tested. It’s a two-step process.
  1. Read the question, but don’t look at the answers. Rephrase the question to make sure you understand it, and devise a plan to solve it.
  2. Solve the problem. Once you have an answer —and only then— see if your answer is listed among the answer choices. By waiting to look at the answer choices until after you’ve solved the problem, you preempt those nasty SAT traps.
We can’t stress enough that if you’re trying to solve the problem directly, you should avoid looking at the answer choices until the end. Since trap answers are often the values you would get at the halfway point of the process of working out a problem, if you peek at the answers, you may get tricked into thinking you’ve solved the question before you actually have.
The Process of Elimination
On every multiple-choice question, the answer is right in front of you. It’s just hidden among those five answer choices. This means you can sometimes short circuit the problem by plugging each answer into the question to see which one works. On certain occasions, working backward could actually be a faster method than just solving the problem directly.
Okay, example time:
A classroom contains 31 chairs, some which have arms and some of which do not. If the room contains 5 more armchairs than chairs without arms, how many armchairs does it contain?
(A) 10
(B) 13
(C) 16
(D) 18
(E) 21
If you want to solve the problem directly, you first have to assign variables:
Total number of chairs = 31
armchairs = x
chairs without arms = y
Next, take these variables and translate them into an equation based on the information in the question:
31 = x + y
y = x – 5
Then substitute one equation into the other:
There you are with the right answer, but it took a bit of time.
What if you plugged in the answers instead? And what if you plugged in intelligently, meaning: First plug in the value C.
Since answer choices on the SAT Math always either ascend or descend in value, starting with the middle value means that you’ll never have to go through all five choices. For instance, in this question, if you plug in C (16) and discover that it’s too small a number to satisfy the equation, you can eliminate A and B along with C. If 16 is too big, you can eliminate D and E along with C.
So let’s plug in 16 and see what happens:
  • The question says that there are 5 fewer armless chairs than armchairs, so if you have 16 armchairs, then you have 11 armless chairs, for a total of 27 chairs.
  • Since you need the total numbers of chairs to equal 31, C is clearly not the right answer. But because the total number of chairs was too small, you can also eliminate A and B, the answer choices indicating fewer numbers of armchairs.
  • If you then plug in D (18), you have 13 normal chairs and 31 total chairs. There’s your answer. In this instance, plugging in the answers takes less time and seems easier.
As you take practice tests, you’ll need to build up a sense of when working backwards can help you most. But here’s a quick do and don’t summary to help you along:
  • DO work backward when the question describes an equation of some sort and the answer choices are all rather simple numbers.
  • DON’T work backward when dealing with answer choices that contain variables or complicated fractions.
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