Math IIC Algebra Strategies
Math IIC Algebra Strategies
There are several ways to answer most algebra problems on the Math IIC. You could try to solve a problem by setting up and solving an equation. Alternatively, you can look for shortcuts in the problem that allow you to find the solution without a lot of math. Finally, you can often substitute numbers from the answer choice and use the process of elimination to discover the right answer.
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 problem that has you stumped 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. To really get the most out of your practice tests, you should analyze not only the questions you get wrong, but also the questions you get right to make sure that you solved them in the quickest way.
We’ll thoroughly explain the different problem-solving approaches, and you can decide for yourself which method to choose.
Let’s use a sample algebra problem to illustrate these varying approaches:
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?
(A) 1
(B) 3.5
(C) 4
(D) 4.5
(E) 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.
Substitution
Sometimes you might be unsure about how to approach a problem or don’t have the time to think out the proper equations. In such instances, substitution might be the best method, especially with 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 information holds true.
The process of plugging in is simple. First, you should make full use of the fact that the answer choices on the Math IIC are always presented in ascending or descending value. So you should almost always 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 25050 = 5 hours to drive to Giambia City. So, if it takes him C 4 hours more to drive, then 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.
Picking Numbers
Picking numbers is a variation of plugging in and should only be used when the answer choices contain variables. A modified version of our original sample question shows what kind of problems lend themselves to picking numbers.
A baseball player travels from his home city, Jasonville, to Giambia City for a baseball game. He drives at m miles an hour. After the game, he flies home instead, traveling at p miles an hour. If the distance from Jasonville to Giambia City is v miles, and it took him j hours longer to drive than to fly, what is j?
(A)
(B)
(C)
(D)
(E)
This question asks you to figure out which set of variables correctly solves the problem. But thinking in terms of variables can sometimes be unintuitive. Picking numbers allows you to transform variables into concrete numbers.
To use the picking numbers method, you need to select numbers and plug them into the answer choices. You’re essentially trying to eliminate the variables from the problem by replacing them with numbers that retain the relationships of the variables. It doesn’t matter what specific numbers you plug into a problem. The same answer choice will always surface as long as you plug in consistently and follow all guidelines given by the problem.
For example, in the above problem, let’s choose to let m = 5, v = 100, and p = 10. Clearly, these numbers aren’t realistic (who flies at 10 miles an hour?), but your goal is to pick numbers that are easy to manipulate. Using these numbers, you’ll see it takes the baseball player 1005 = 20 hours to drive and 10010 = 10 hours to fly. So, it takes him 20 – 10 = 10 hours longer to drive. Now all you have to do is replace v, p, and m in each of the answer choices with 5, 100, and 10, respectively. You are left with simple arithmetic expressions, and only D produces an answer of 10.
Very rarely, more than one answer choice will result in the correct answer for the first set of numbers you picked. When this occurs, simply plug in a different set of numbers. You will almost never have to plug in more than two sets of numbers.
When picking numbers, you must check through all the answer solutions with your chosen numbers. Obviously, this will slow you down, but that’s the price you pay for using this method. Picking numbers gives you a mechanical method for solving tricky problems and also allows you to check your math for careless calculations.
Finally, when you are picking numbers, avoid 0, 1, or any numbers that already appear in the answer choices. You should also make sure that you try to use a unique number for each variable. Otherwise, you can oversimplify the expressions you are dealing with and accidentally pick the wrong answer.
The Bottom Line
As you can see, there is no “right” method to solving all algebra problems. Some methods work better than others, depending on the question. Part of your practice for the Math IIC test will help get you comfortable with algebra questions so that you can quickly choose which method you want to use for each question.
Now we’ll review the algebra topics covered in the Math IIC Subject Test.
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