Question

Dear Mitch,

I'm taking the PSAT and the SAT for the first time this school year, and I've heard so much about all these "tricks" people know that they say make most of the questions so easy to figure out. (Even some of the hardest ones on the whole test, but only if you know the tricks.) But I started looking through a book my brother used, and he always said it had a lot of the good tricks in it and he read them and practiced them, and now he's in a fairly decent college so he might be right in a way. But when I look through the book and read some of the tricks all the way through, I don't think that remembering them plus knowing when to use them and doing it right would be any easier or faster than just studying what you have to know from school and then doing the problems the normal way. I know you and my teachers always say "everybody's different, so it depends," but, honestly, if you weren't taught the tricks in school is it really something you can get good at in a couple of months before the test?

From Jacob

In Orange County

Answer

Dear Jacob,

Thank you for sending in your question. It is the kind I love, in part because it's an issue I've found myself considering, and it's one of those questions that touches upon a whole web of related questions that intrigue me.

Before I dart into the answer, I have to tell you something: You've come to the right place for your answer. I happen to be one of the weird ones who loves tests like the SAT, but even more than the test itself, I LOVE teaching others how to take the test.

Here Goes:

First, I think it can help everyone's attitude toward the test and approaching it as the fun game it can be if instead of thinking of the sort of quick, clever approaches to questions as "tricks" we think of them as techniques. After all, that is really what they are, as most of these little methods come from fundamental concepts that people either forget about as the work grows more complicated or they never really understood the logic and underlying simplicity of all the scary-looking formulas and symbols they have to deal with in the usual school math curriculum. In other words, you could have all the weird-looking symbols in the world, but if the question can be boiled down to something like this: 2 + 3 = ?, you can pretty much assume that no matter how fancy such simple numbers are disguised by formulas and strange symbols, 2 + 3 = 5.

Second, remember that one of the main challenges of this test for many students is that you not only have to answer all kinds of questions that are designed to look as unfamiliar as possible, but you have to do them pretty fast. You may get the hardest one right, and you may be the only one in the country to get it right, but if you get most of the others wrong, or run out of time before you get to most of the other questions because you were busy being a genius on that one hard one ... well, too bad; you'll be taking the test again next time. So the time factor does make the test into a bit more of a game than math in school usually is, where the most valued aspect usually is the understanding, the intelligence of the approach you take to a problem, and how neat and organized your work is, so that it can readily be checked to find any errors -- if there are any.

On the SAT, your answering style or method will never be checked by anyone for neatness. You can scribble like a maniac, but if you fill in the right oval with your #2 pencil, you got it.

O.K., enough talk. Let's look at a real problem that was on a recent SAT exam, though I've changed the numbers and other insignificant parts to avoid any issue of plagiarism.

QUESTION:

293,561 x 279 =

A.

B.

C.

D.

E.

WHAT?

QUESTION: How are we supposed to do it when the choices are blank?

ANSWER: Hold on, I'm getting to that part, but I'm trying to make a point here.

POINT: You can do this one on your calculator, obviously, though it might take you almost half a minute. Now, that may not sound like a lot of time, but for this one it seems to me to be too much time to waste. Why? Because there will be some really hard ones on the test that you may need several minutes to do, and so you'll want to do whatever you can to save time on any of the easier ones to accumulate all those extra minutes... So...

Remember When Sesamee Street used to do "Which one of these things is not like the other?" And they'd show, perhaps, a picture of a doughnut, a picture of a wheel, a picture of a nickel, and a picture of a triangular hat (presumably for a person with a triangular skull)...

O.K., well that can be a very helpful idea on the SAT. Which answer choice is somehow different from the others in some mathematical way?

Let's see...

Say the choices for the above question were as follows:

a. 82,903,428

b. 81,903,426

c. 81,801,112

d. 81,903,419

e. 81,775,314

Huh?

Well, as you may recall from kindergarten (though probably not) most of math is a bunch of patterns.

Such as:

Odd number x odd number = odd number (example: 3x5 = 15)

Odd number x even number = even number (example: 3x4 = 12)

Even number x odd number = even number (example: 2x3 = 6)

Even number x even number = even number (example: 4x6 = 24)

So?

Let's take another look at the question, but, even more importantly, let's take another look at the answer choices...

First, though, a review of another mathematical fact:

Any number, no matter how long or short it is, that ends with a 0 or a 2 or a 4 or a 6 or an 8 is an even number.

And...

Any number, no matter how long or short it is, that ends with either a 1 or a 3 or a 5 or a 7 or a 9 is an odd number.

And that's it. There are no other possibilities for the last digit of a number in our system. So here we have a number that ends with a 1 (and therefore an odd number), multiplied by a number that ends with a 9 (and therefore also an odd number), so we have an odd number x an odd number, which means our answer is going to be an odd number. That means the answer will end with a 1 or a 3 or a 5 or a 7 or a 9. Now, before going to your calculator, take one more look at the answers.

Only one of the choices ends with an odd number, the number 9: Choice D.

Now, if you'd like, you can take out your calculator to check our work!

This should give you a feel of how techniques could help a lot on a timed multiple choice test.

Hope that helps,

Mitch