When to Use the Most Common Math Strategies

There are three very basic math strategies for standardized tests that every high school student should know: Plugging In Answer Choices, Taking Guesses, and Picking Numbers. Take a look at these links before you continue with this message, as the information below will make more sense after a quick review of these strategies.

Sometimes students get confused about when to use which of these strategies. Although there are no definite rules I can give you that will work 100 percent of the time, today I will provide you with some general guidelines.

Plugging In

Let’s begin with the strategy of plugging in answer choices:

This strategy can only be used for multiple choice questions. You simply plug each answer choice into the question until you find the one works. It is always best to start with choice C as your first attempt, unless there is a specific reason not to (on the new SAT you can start with choice B or C, as there are now just four choices). An example of such a reason would be that the word “least” appears in the problem. In this case start with the smallest answer choice (which will usually be choice A or E). Similarly, if the word greatest appears in the problem, start with the largest answer choice.

Plugging in can be used on problems from every topic and difficulty level. It’s often a great way to avoid having to perform messy algebra.

This strategy is most useful when the last part of the question says “What is_____” where the blank contains a single quantity.

Here are some examples:

(1) What is the value of x?
(2) What is the length of the original rectangle?
(3) What is the second number in the list?
(4) Which of the following is a perfect cube?
(5) What is the least such value of x?

For the first four of these examples you would start with choice C. For the fifth example you should start with the smallest answer choice.

This strategy is generally NOT useful when you are asked to find a more complicated expression. For example, do not try to plug in answer choices if the question ends with

“What is the value of x + y?”

In this case you will probably want to use the strategy of “Taking a guess,” or possibly “Picking numbers.”

During your SAT math practice sessions, you should try to apply this strategy on every multiple choice question. The more you attempt to use it, the easier it will be to detect when it can be applied.

Here is a straightforward example of a Level 1 Number Theory problem where “starting with choice C” is a useful strategy.

Three consecutive integers are listed in increasing order. If their sum is 138, what is the second integer in the list?

A. 45
B. 46
C. 47
D. 48
E. 49

I suggest you try to solve this problem in 3 ways:

• by starting with choice C
• algebraically
• using the fact that in a list of consecutive integers, the arithmetic mean is equal to the median.

And here is a Level 4 Geometry problem where this strategy is effective:

The sum of the areas of two squares is 85. If the sides of both squares have integer lengths, what is the least possible value for the length of a side of the smaller square?

A. 1
B. 2
C. 6
D. 7
E. 9

You should solve this problem by starting with choice A.

There are more examples in my original blog post titled Plugging in Answer Choices.

Taking Guesses

Next let’s talk about the strategy of taking a guess:

This strategy is similar to plugging in, except with this one you are not using the answer choices. The reason you are not using the answer choices is either because it is a grid in problem (so there are no answer choices), or the question is asking for a more complicated expression such as “the value of x + y,” or “the perimeter of a geometric figure.” In the first case you may want to take a guess for x or y, and in the second case you may want to take a guess for the width of a side of the figure. For examples of applying this strategy see my original blog post titled Taking A Guess. For a more difficult example, see my blog post titled Taking a Guess – A More Difficult Example.

Picking Numbers

And finally, let’s talk about the strategy of picking numbers:

This strategy is applied by choosing specific values for the unknown quantities in the problem. A new problem is formed that is easier to solve. After solving this easier problem, you must then plug the specific values you have picked into every answer choice, and eliminate any answer choices that do not come out correct. If more than one answer choice has not been eliminated, you can try picking new numbers to eliminate more choices.

Here are some occasions when the strategy of picking numbers will usually work:

• When one or more variables appear in the answer choices.
• When the word “percent” is in the problem (pick 100).
• When there is a variable in the problem, and it is implied that the answer does not depend on the value of the variable.

Here is an Algebra problem where “Picking numbers” can be used.

Which of the following is equal to (x + 66)/22 ?

A. (x+33)/11
B. x+3
C. 3x
D. x/22+3
E. (x+3)/11

Note that you usually want to avoid picking numbers that are too simple. For example, if you choose x = 0, then the answer to the question becomes 3. Now, if you plug a 0 in for x into every answer choice you get the following:

A. 3
B. 3
C. 0
D. 3
E. 3/11

Note that A, B and D are all correct.

See if you can solve this problem by picking a better number. You may also want to try to solve it algebraically.

For examples of applying this strategy see my original blog post on Picking Numbers.

Picking Numbers In Percent Problems

If the word “percent” appears in a problem it’s usually a great idea to choose the number 100. This often works even when there is no variable in the problem.

For examples of picking numbers in percent problems, see my blog post titled Picking Numbers In Percent Problems.

Summary

To summarize, here are some general guidelines for choosing which strategy to use:

• If the answer choices are all numbers, and you are being asked for a simple quantity, try plugging in first.
• If the answer choices are all numbers, and you are being asked for a more complicated quantity, try taking a guess.
• If the answer choices contain variables, try picking a number.
• Any question that mentions percents, pick the number 100.
• In grid in questions with variables, try taking a guess.

There is a lot of information in this blog post with links to many of my other posts, so take your time to read and digest the information. As always, the best way to internalize the concepts above is by practice. For daily practice you may want to check out the Get 800 collection of test prep books. Click on the picture below for more information about these books.

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