SAT Math Study Tip # 2

Sat Math

Math questions that involve algebra on the SAT can present students with a bit of a dilemma, which is, “should I try and solve this problem using algebra, or should I try and work ‘around’ the algebra?”  A smart study plan should include ample time to practice all the ways that algebra can be avoided.

Why is this?

There are two good reasons to avoid algebra as much as possible in your problem-solving. First, even if the algebra needed is straightforward, it will often take longer to solve the problem using algebra than with other methods. Second, many times the algebra needed is not at all obvious to a student, and may even require a creative use of algebra (horrors!).

Either way, using numbers to reason through a problem, instead of algebra, makes it easier to understand the problem, and to “track” your reasoning. Most of all, the “Choose Numbers” strategy allows students to do the first step to do in a problem quickly, and as all test-writers know, the first step is often the hardest one.

Sat Math Prep

Now, let’s see how to practice using the “Choose Numbers” strategy in our study time for the SAT:

Here’s how it works:

Q:  Betty is 4 years younger than Bill. If Bill is  years old, how old will Betty be 7 years from now?

Now, if we tried using algebra to solve this, we would hope to think of something like the following:  Let Betty’s age = x,   then Bill’s age =x-4  …and so on…

Let’s choose numbers instead:

If we choose 10 years old for Bill (since he is the “x” person, this means we choose ), then Betty is 4 years younger, so Betty would be 6 years old (10-4).

So, 7 years from now, Betty will be 13 years old (6+7). Since the question asks us how old Betty will be, the correct answer on the list of choices will be the one that equals 13, after substituting in x=10

The correct choice that will appear on the list of choices will be:   x+3

 

Q:  The sum of 4 odd consecutive integers is S. Find the sum of the next 2 consecutive even integers that follow this sequence.

If we were trying to use algebra to solve this, we would hope to think of something like the following:   x+(x+2)=(x+4)…and so on…

Let’s choose numbers instead:

The four odd consecutive numbers could be 3+5+7+9=24….So, S = 24

Then, the next two even consecutive numbers would be 10+12 = 22      

Since they asked for the sum of the two even numbers following the sequence, the correct answer on the list of choices will be the one that equals 22, after substituting in S = 24

The correct choice that will appear on the list of choices will be: S-2

It is often surprising to students how good they can become with this strategy, if they practice using it enough. Don’t get discouraged if it doesn’t work all the time (neither does algebra). To ensure that time isn’t wasted trying to use this strategy on problems where it won’t work (and wasting precious study time), here is an example of a question type where this strategy won’t work.

In this case,  x and n are part of an equation, and only have one correct value. We can’t just choose numbers, because even if we tried, we couldn’t get then to “work”, i.e. the numbers that we chose would not make the equation true. We would have to use a different method for this one.

Remember that using the Choose Numbers strategy is the best way to avoid difficult and time-consuming algebra, and to get the first step of a problem done quickly. If you are a student who loves algebra and can use it as a problem-solving tool quickly and efficiently, then you might only use the Choose Numbers strategy as a back-up (like a Plan B), if you can’t get the algebra to work. For everyone else, think of avoiding algebra as an “art”, and the Choose Numbers strategy as one of your best techniques.