The Legendary Zero (0)

Before we get started, let's define "Zero".

Zero from Megaman Zero

As awesome Megaman Zero is, no, not this Zero.

Zero from Borderlines 2

Not this Zero either...

Zero from The Nightmare Before Christmas

Nope, not looking for this Zero.

YES. The number zero is what I am talking about.

Zero is a quirky number; it has many strange properties that not too many students remember, and the SAT loves to use those obscure concepts against test takers. So here is a problem from The Official SAT Question of the Day, January 28. 

How to solve this question:

If you are familiar with the properties of zero, you should find this question really easy. Easy enough to figure out the answer in your head. 

I want you to take out a calculator. It doesn't matter what type of calculator it is. Don't have one? Use the calculator on the device that you are using right now (computer, smartphone, tablet, PSP, etc.)

You can't get an answer, right? That's because any number divided by 0 is undefined; no number can be divided by 0. 

Just in case I didn't made any sense, let me elaborate.

The denominator is (x-c). For any fraction, the denominator is basically the number you divided with. So we have to find the value of x that makes (x-c) = 0, which makes the fraction undefined. 

It is given that c is bigger than 0: a positive number. This is important, because if c were to be a negative number, we would have some problems in solving the question.

First case: if x were to be a positive number, subtracting the x with a negative c would be (x+c), because subtracting a negative number changes the operation into addition.

Second case: if x were to be a negative number, we would be adding two negative numbers together, thus making a smaller negative number.

Thanks to the problem giving us the condition that c is a positive number, all we have to do is plug in a value that is equal to c to x because we want the denominator to equal 0, which is undefined. 

For this problem, plugging in c for x would give us (c-c) = 0, making the fraction undefined. 

Therefore, the answer is (C) "III only". (What a coincidence.)

As you can see, the SAT made a rather obvious question look complicated by using only letters instead of numbers. If you want to score well on the SAT Math, you have to be able to see through the camouflage the SAT puts on the questions. In order to do so, basic math concepts have to be second nature to you. When you are familiar with those basic math concepts, you will be able to recognize the solutions to SAT Math problems effectively and efficiently. 

Here are some rules of zero that you should know for the SAT. These should be familiar to you, assuming your math teachers taught you well...

Rules of Zero

- 0 is an even integer

- 0 is neither positive nor negative

- 0 is a multiple of every number

- 0 is not a prime number

- Any number multiplied by 0 is 0 (ex: 896 x 0 = 0)

- Any number divided by 0 is undefined (ex: 564 ÷ 0 = undefined)

- Any number that is to the 0 is 1 (ex: 215⁰ = 1)

- 0 to the any power is 0. Except to the 0, which is undefined. (ex: 0¹² = 0, 0⁰ = undefined)