6.5 SAT Math - Must/Always Questions

There are certain types of questions tested on the SAT for which you need a specific strategy.  These types of questions will either actually say "what values of x must be true?" or imply it, or they may appear as Roman Numerals questions that look like this:

13. If s is divisible by 3 and t is divisible by 7, which of the following must be divisible by 21?
I.   st II.  3s + 7t III. 5t + 3s

For these SAT questions, you need to understand that you can NOT simply select an answer and move on.  You need to attempt to disprove all the answer choices; the one that you cannot get rid of is the answer.  These types of questions are specifically testing your creativity, so get creative!  Try to break patterns and trends that you notice, as long as you obey the limits set by the question.  How can you mix it up easiest?  By trying numbers from each category in the following order:
1) normal numbers 2) zero 3) one 4) negative numbers 5) fractions

This is the quickest and simplest way to eliminate answer choices.

Let's try it with the following question:

13. If, m ≤ 0 which of the following must be an even integer?
I. m²
II. -m(1 + m) + m(1 + m)
III. 2m/m

(A) I only (B) I and II only (C) II only (D) II and III only (E) I, II, and III

Well, the question prohibits us from trying a positive normal number, so let's try a negative normal number, like -3.

Which roman numeral should you cross off?  That's right, the first one.  But you should also go down to the answer choices and cross off A), B), and E).  Since they contain Roman Numeral I, they can't possibly be right. 

You may be tempted at this point to go with your hunch and select D), but don't!  Go to the next number on the list and try zero.

What happens?  You'll still get zero for Roman Numeral II, but for Roman Numeral III, you will have to divide by zero.  Is that possible?  No, it isn't.  Because of that, you can cross off both III and D), and you are left with C) as an answer.

As you can see, you sometimes CAN'T use the whole list because of the limits given in the question.  But don't stop with just one try!  If the question says you can only try positive integers, fine, but always try at least three combinations of numbers before selecting an answer.  If you can go down the list, fine, but if you can't, mix it up.
-SAT Math Hint: Use your creativity!  Try to break any patterns you may be forming.  If you are given the relationship a < b < c < d, try 1, 2, 3, and 4 for your numbers, but also try 1, 2, 599,999, and 1,000,000.   Try not to always put things in consecutive order, or try to use weird fractions like 91/99  instead of always using the common ones like 1/2.  Again, the whole point is to disprove as many options as possible, not to get through the question quickly!  So try to think of any situation in which one of the choices you've found would not work.

If you're worried about how long this takes, don't be.  Once you have the list memorized, it actually goes pretty quickly, especially because, as seen in the example above, oftentimes you won't even need to go down the whole list because you've answered the question already.  Have it memorized and use it whenever you are given a question in which more than one number can and should be tested.  No matter how the question is worded, ask yourself, "Does the answer have to be true?"  If not, go down the list.