Though there are four types of questions on the Math IC, there is a standard procedure that you should use to approach all of them.
- Read the question without looking at the answers. Determine what the question is asking and come to some conclusion about how to solve it. Do not look at the answers unless you decide that using the process of elimination is the best way to go.
- If you think you can solve the problem, go ahead. Once you've derived an answer, only then see if your answer matches one of the choices.
- Once you've decided on an answer, test it quickly to make sure it’s correct, then move on.
Working Backward: The Process of Elimination
If you run into difficulty while trying to solve a multiple-choice problem, you might want to try the process of elimination. For every question, the answer is right in front of you, hidden among 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:
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A classroom contains 31 chairs, some of 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? |
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(A) |
10 |
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(B) |
13 |
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(C) |
16 |
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(D) |
18 |
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(E) |
21 | |
Given this question, you could build the equations:
Then, since y = x – 5 you can make the equation:
There are 18 armchairs in the classroom.
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 is 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 we have 16 armchairs, then we would have 11 normal chairs and the room would contain 27 total chairs. We needed the total number of chairs to equal 31, so clearly C is not the right answer. But because the total number of chairs is too few, we can also eliminate A and B, the answer choices with smaller numbers of armchairs. If we then plug in D, 18, we have 13 normal chairs and 31 total chairs. There's our answer. In this instance, plugging in the answers takes less time, and just seems easier in general.
Now, working backward and plugging in is not always the best method. For some questions it won’t be possible to work backward at all. For the test, you will need to build up a sense of when working backward can most help you. Here's a good rule of thumb:
