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Math SAT Preparation – Logic and Number Tricks

Welcome to a Math SAT Preparation Lesson. In this lesson we will go over some logic and number tricks that can help you out when writing you math SATs.

Let’s start with a simple yet confusing concept- counting

I don’t know about you, but I always mess up counting. If I’m counting from 6 to 89 inclusive, how many numbers are in there? How should I know? Is it 89-6, or 89-6+1, or maybe 89-6+2?

The trick is to always think about what you’re doing. When you’re counting numbers from x to y inclusive, you’re counting x, x+1, ..., y. When you do y-x, that first x doesn’t get counted, kind of like the 0 when you’re counting from 1 to 10. So you need to add one to the whole mess. In short, the formula for counting from x to y inclusing is y-x+1.

Moving on to trickier counting

Some questions require you to count events that grow or shrink by a certain factor, such as a bus with twice as many people getting on at each station. To count these type of situations, you have to multiply your original amount by the factor given each step. If you’re working backwards, trying to figure out something like the amount of people that were on the bus originally, all you have to do is divide by the factor given.

Some situations require logical thinking. The one I find most annoying is the handshake question- say 5 people meet and they all shake hands with each other, how many handshakes happen? You have to realize that won’t work, since each person won’t shake his own hand, so the answer is , but since person A shaking hands with person B is the same handshake as person B shaking person A, we divide the whole thing by 2, to get . This type of counting is annoying, so think of the situation logically, and don’t be embarrassed to use your fingers.

Here come the cool number tricks of divisibility

You may already know these, but if you don’t, here are some cool divisibility tricks:

1. A number is divisible by 2 if it’s even.

2. A number is divisible by 3 if the sum of its digits is divisible by 3.

3. A number is divisible by 5 if it ends in a 5 or a 0.

4. A number is divisible by 6 if it’s divisible by both 2 and 3.

5. A number is divisible by 9 if the sum of its digits is divisible by 9.

6. A number is divisible by 10 if it ends with a 0.

7. A 2-digit number is divisible by 11 if its two digits are the same. A 3-digit number is divisible by 11 if the inner digit is the sum of the outer ones. Generally, a number is divisible by 11 if when you add the first digit, subtract the second, add the third, subtract the , etc. you get 0 or any other number divisible by 11.

These tricks are nice to know because they can save you time, as you can just look at a number and tell what his divisibility is without using your calculator at all.

Finally, some digit game concepts

Digits are cool. They represent the following group: 0,1,2,3,4,5,6,7,8,9. All numbers are made of digits. But we can represent numbers using more than just digits. For example, say x is the digit 1, y is the digit 2 and z is the digit 3. Then means . If you’re trying to solve this kind of puzzle and find out what each digit is, you may want to start at the left-most side and move right.

Let’s look at an example- say a,b,c are all digits and .The only digit that added to 4 results in a 2 is 8, so . Then we continue to find that and .

Other cool digit games you may be familiar with include the suddenly-popular Soduko, but I’ll leave that to people who actually play the game in their spare time. I have more fun stuff to do.

So, ready to twist your brain-wheels and prove your might? Attempt and “Logic and Numbers test”: .