5.2 SAT Math - Rules

Now to the SAT math rules.

1. Keep your work neat and organized.  This is the only form of insurance you have, and the only way you can possibly notice if you made an easily fixable careless mistake.
2. Know what number the answer choice represents.  This goes back to one of our first rules, rereading the bottom of the question before answering.  You want to make sure that you're looking for the correct thing.  If the question states "A hamburger and soda cost $4.75.  If the soda costs $.75 less than the hamburger, how much does the hamburger cost?"  you need to make sure that you're looking for and answering the cost of the hamburger, not the cost of the soda.
3. Make sure your answer is true for ALL parts of the question.  Some of the questions in which it is most convenient to Use the Answer Choices are long and complicated with many elements to satisfy.  The answer you select must be true for all of them, not just one or two.
4. Stop when you get an answer that works.  Unlike ITOS, when you Use the Answer Choices, there can only be one right answer.  When you find it, you're done.  Move on.  Don't waste time checking the other guys.  They're wrong.  Is that clear enough?

Example Problem

Let's see how this works on one that's a little easier.
6. If the average of 8, 8, 10, 14, and x is x, what is the value of x?
(A) 8
(B) 9
(C) 10
(D) 12
(E) 14

Let's start with answer choice (A).  Try 8 for x.  Following Rule #1, write down the equation you're trying right next to the answer choice.  It may seem tedious and annoying, but so is messing up something careless.  So the math will be .   Is that true?  Write "No" next to the answer choice.  So your paper should know look something like this:

      6. If the average of 8, 8, 10, 14, and x is x, what is the value of x?

Let's try (B).  .  Does it work?  Write "No"
Let's try (C).  .  Does it work?  Yup.  You're done.  Pick (C).

On easier SAT questions like the one above, it's fine to just keep your neat work right next to the answer choices, but on more complicated questions, it's good to have some sort of chart to keep track of everything you're trying.  Take a look at this one:

Example Problem 2

16. In typing class, Steve and Sally began a quiz at the same time and worked at a constant rate of 80 words per minute (wpm) and 85 wpm respectively.  If Steve finished the quiz 3 minutes after Sally, how many words were on the quiz?
(A) 51
(B) 240
(C) 1360
(D) 4080
(E) 4335

There's a few things to keep track of here, so let's make a quick chart:

Why time on the chart?  Because we need to divide the number of words on the quiz by the number of words per minute to see how long the quiz took each of them, and see if that difference is 3.  Let's start with (A).

Keep track of your work on the chart, listing which answer choice goes with each row so that you don't forget or lose track.  Doing the math, we get 51/80 = .6375.  Now it may seem highly unlikely that he took a test that fast, and you're right, this doesn't look like the right answer, but work out Sally's time anyway.  It's better to take the extra five or ten seconds to confirm your hunch than to skip to the next answer choice, try all five, only to have to come back and redo your work on this one later if nothing else worked.  So for Sally: 51/85 = 6.  Yeah, there's no way this is the right answer.  Fill in the chart and move on to (B).

Let's do the work:
  Does the difference between 3 and 2.82 work out to 3 minutes?  No, but we're getting closer.

  No, but again closer.  Let's try (D): .
Does 51 - 48 = 3?  Yes!  We have our answer.
 

This may seem like it's going to take a while, but once you get the hang of it, it's really a very quick, easy way to solve more difficult problems.  Also, keep in mind that you do not have to start at A).  You can start at any answer choice you like as long as you try all parts of the question.  Do NOT start at B), work it out halfway and then say, "No, I don't think this is working," and try D) for a while, and then say, "Wait, maybe I should have started with A)…"  That's going to take you forever and not help you.  Pick an answer choice to start with; if that doesn't work move on to the next one.  BE METHODICAL.  Jumping around is why most people get confused.

If you knew how to set up the previous example and are rolling your eyes at this SAT Strategy as if everyone else is just idiots and you are so superior and so smart that you don't need Strategies... don't be so quick to dismiss it.  In addition to being very helpful for when you get confused or aren't sure if you're doing a problem right, Using the Answer Choices is also extremely helpful to simply give yourself a break.  Remember, the SAT is almost 4 HOURS LONG.  That's huge.  Your brain is going to be exhausted.  And the test starts at 8 a.m.  You are going to be exhausted.  Every now and then, when you get to a complex problem, take a break.  Sure you could do the algebra, but Using the Answer Choices will take you the exact same amount of time with less work.  Let your brain rest for twenty seconds before moving on to the others.

By the way, Using the Answer Choices works really well for Geometry questions, too, especially because triangles must have a certain number of degrees, etc.  If you know your basic Geometry rules (which we'll get to in that section), you can get an answer pretty quickly by Using the Answer Choices.

So let's get back to Algebra.