There are several ways to answer most algebra problems. You could try to solve a problem by using standard algebra and setting up and solving an equation. Alternatively, you could try to avoid algebra and simply plug the answer choices back into the question until one of them works out. Or you can pick numbers to substitute into the various expressions given as answer choices.
None of these methods is necessarily better than the others. Remain flexible in your approach to each question and choose the method that best suits the problem. For a problem you know how to solve, using algebra is probably the quickest method. In contrast, a tough problem that you are unsure how to solve might become easy if you try to plug in some answers. When you study your practice tests and look over the algebra questions you got wrong, you should think about the method you employed. Did you plug in answers when you should have used algebra? Did you use algebra when you should have plugged in answers?
We’ll lay out for you the different problem-solving approaches and tell you all you need to know about them. Then you can decide for yourself which method to choose.
Let’s use a sample algebra problem to illustrate these separate approaches:
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A baseball player travels from his home city, Jasonville, to Giambia City for a baseball game. He drives at 50 miles an hour. After the game, he travels back home and takes a flight that travels at 500 miles an hour. If the distance from Jasonville to Giambia City is 250 miles, and it took him j hours longer to drive than to fly, what is j? |
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(A) |
1 |
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(B) |
3.5 |
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(C) |
4 |
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(D) |
4.5 |
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(D) |
12 | |
Using Algebra
This question is a simple rate problem that can be solved with a few basic equations. Since traveling time = distance
speed, it took him:
to drive to Giambia City. To find the duration of his flight, we use the same rate formula:
It took the player:
longer to drive. D is the correct answer.
Plugging In Answers
Sometimes you might not be sure how to approach a problem or don’t have the time to think out the proper equations. In such instances, plugging in might be the best method for you, especially as you come across the more difficult questions at the end of the test. All you have to do is substitute the answer choices back into the problem, and see whether the given
iholds true.
The process of plugging in is simple. First, you should make full use of the fact that the answer choices on Math IC are always presented in ascending value. So start by plugging in answer choice
C, since if it doesn’t turn out to be the answer, you can usually tell whether to try a smaller or larger answer choice. Now, to solve the question: it takes the baseball player 250
50 = 5 hours to drive to Giambia City. So, if it takes him
C 4 hours more to drive, than it takes him 5 – 4 = 1 hour to fly back to Jasonville. But the question tells us that in 1 hour, he could fly 500 miles. Therefore, it must take him longer than 4 hours more to drive than to fly. Next, we try
D 4.5. It takes him 5 – 4.5 = .5 hours to fly, which means that he travels 500
.5 = 250 miles on his flight.
D is the answer.
