Question

Dear Mitch,

A couple of days (I think it was a couple of days ago, anyway) you answered a question about alphanumeric problems on standardized tests, and that was pretty cool because there's not all that much they teach about it in school, and I don't think it's even in the SAT book my father got me (and it's one of the famous ones!).

Anyway, I think it was toward the end of your answer, you said something about there being lots and lots of rules that can be used to help you figure out what number the letters are supposed to be. But then you didn't get to any more than the one you explained. I'm sure there really are a lot of tricks for those, and I'm not saying I would even want to try to remember them all, but if you gave just like one or two I think I'd get an idea how to figure out a bunch more on my own. Just a thought, but I would bet other kids would want more too.

I check in every day and started collecting your SAT tips in a binder.

Sincerely,

Sean O.

Columbus, Ohio

Answer

Dear Sean,

Yes, I agree that knowing a few alphanumeric concepts can help you figure out more on your own, so here's one:

Say that the first expression they give you is one like this:

b x b = cb

(And I have seen this very one form part of a bigger and more complex question on several exams, so it's worth knowing!)

Okay, so what is it telling you?

It's telling you that there is a single digit number that produces a double-digit number when it is multiplied by itself (squared).

So, if you look at the digits one at a time, you realize that b cannot be 0 or 1 or 2 or 3.

Why? Because, when you square 0 you get 0, when you square 1 you get 1, when you square 2 you get 4, and you square 3 you get 9. So the square of 0, 1, 2, and 3 gives you single-digit answers. But when you square 34 you get 16, which is a two digit number, and therefore, of course, you get a two digit number when you square anything larger than 4 (5,6,7,8,9). Remember, there are only 10 choices for any digit in our math system.

What else does b x b = cb tell you?

It tells you that the two-digit number you get for your square has the same number for its second digit (one's place) as it does when it is its own number. So, how does that help? Well, of the list we came up with of single digit numbers that square to give a two-digit number, only two do that. Which ones? Well, 5 x 5 = 2__5__ and 6 x 6 = 3__6__

But you want one answer and you have two possibilities. Then what? It depends. The question probably gives other parts to work out, and you will see that only one of the choices you have (5 0r 6) will work with the other equations. OR, if it is a multiple choice, they could present it like this: Which of the following Could be b? And the choices are: 2, 4, 6, 8, 9. Since 5 is not an option, the viable one is 6. Likewise, if the choices are 1, 3, 5, 7, 9, then 6 is not an option. The answer would have to be five.

__But NOTE__: There is no limit to the way these problems can be presented, and do NOT ever assume you've seen the problem before, because a lot of them look alike at first but turn out to be VERY different. One way this exact concept was tied to another was this: A x A = GA, And A + 2 =an odd number. So, would that mean that A is odd or even? Odd, because the patter is odd even odd even, etc. so, as a logical result of this pattern, any odd number plus two gives you an *odd* number, and any even number + 2 gives you an* even* number.

Little things like this could come in very handy during the exam, especially if you know hundreds of them!

Hope this helps,

Good luck,

Mitch