MC questions are the most common type of math question on the test. These problems involve a mathematical statement or question that you need to solve, followed by five answer choices. Sometimes the problem will include a chart, graph, or geometric diagram. Your job, obviously, is to choose the right answer.

The MCs are split into two groups: 25 in one of the 30-minute math sections and 10 in the 15-minute section. Both groups are organized according to difficulty, so you know the first questions of each group will be easier while the last will be harder.

The procedure to follow for answering individual MCs is not that different from the one we described for answering sentence completions and analogies.

If you run into difficulty while trying to solve an MC, you might want to try the process of elimination. On every question, the answer is right in front of you, hidden among those five answer choices. So if you can’t solve the problem directly, you might be able to plug each answer into the question to see which one works.

Not only can this process help you when you can’t figure out a question, there are times when it can actually be faster than setting up an equation, especially if you work strategically. Take the following example:

Given this question, you could build the equations:

Then, since y = x – 5, you can make the equation:

This approach of building and working out the equations will produce the right answer, but it takes a long time. What if you strategically plugged in the answers instead? Since the numbers ascend in value, let’s choose the one in the middle: (C) 16. This is a smart strategic move because if we plug in 16 and discover that it was too small a number to satisfy the equation, we can eliminate (A) and (B) along with (C). Alternatively, if 16 is too big, we can eliminate (D) and (E) along with (C).

So our strategy is in place. Now let’s work it out. If you have 16 armchairs, then you would have 11 normal chairs and the room would contain 27 total chairs. We needed the total numbers of chairs to equal 31, so clearly (C) is 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 in general just seems easier.

Notice that the last sentence began with the phrase “in this instance.” Working backward and plugging in is not always the best method. For the SAT, you will need to build up a sense of when working backward can help you most. A good rule of thumb for deciding whether to work backward is:

If the answer choices contain variables, working backward will often be quite difficult— more difficult than working out the problem would be. If the answer choices are complicated, containing hard fractions or radicals, plugging in might prove so complex that the process will be a waste of time.

Substituting numbers is a lot like working backward, except the numbers you plug into the equation aren’t in the answer choices. Instead, you have to strategically decide on numbers to substitute to take the place of variables. For example, take the question:

It might be hard to conceptualize how the two variables in this problem interact. But what if you chose two odd numbers, let’s say 5 and 3, to represent the two variables? Once you begin this substitution it quickly becomes clear that:

By picking two numbers that fit the definition of the variables provided by the question, it becomes clear that the answer has to be (D) since the equation equals 225. (By the way, you could have answered this question without doing the multiplication since two odd numbers, such as 9 and 25, when multiplied, will always result in an odd number.)

Substituting numbers can help you transform problems from the abstract into the concrete. However, you have to remember to keep the substitution consistent. If you’re using a 5 to represent p, don’t suddenly start using 3. Also, when picking numbers to use as substitutes, pick wisely. Choose numbers that are easy to work with and that fit the definitions provided by the question.