All too often, I find students reluctant to pick numbers when trying to solve a problem. Some balk saying, “Doesn’t that take too much time.” Others exclaim, “Are you allowed to do that?”

So the bottom-line: if you want to be successful on the SAT math section, plug-in whenever you can. And if you are unsure whether a problem lends itself to plugging in, plug in! Don’t hold back and dilly-dally, unsure how to approach a problem. That wastes time.

For instance, a great problem type to plug in involves variables and inequality signs, arranged with Roman Numerals. The words MUST BE TRUE or COULD BE TRUE accompany the problem. Let’s have a look:

1. If a > b > c, and a, b, and c are integers, which of the following MUST be true.

I. >

II. <

III. is even.

(A)  I only

(B)  III only

(C)  I and II

(D) II and III

(E)  All of the above

Explanation:

For (I) if we plug-in any numbers, this equation will always hold true. Note we can drop b from both sides of the equation. If you unsure, plug in numbers. (I) MUST always be true.

For II, your initial hunch is that this condition MUST be true. However, do not simply rely on your first instinct (it may be wrong). Plug-in and test using numbers. Remember, ‘MUST be true’ means that the condition must hold in every case. If you find that one exception, then the condition must not always be true. If you plug-in a negative number for b that has an absolute value that is greater than a, then you have found a case where (II) doesn’t hold true. For instance, plug in -2 for b, and -1 for a. And we have a case where b is greater than a.

For III, plug-in a = 3, b = 1, c = 0. Just like that we’ve found a case where III is odd.

Therefore the answer is (A) I only.

Takeaway

When dealing with variables presented in three Roman numerals, plug-in. It will make the question much less abstract and help you quickly hone in on the right answer.