Quick Division on the SAT Test

Some questions involve being able to quickly divide one number by another. Of course, the SAT is not really testing your ability to do long division, although you are welcome to use long division in a jam. If you tried to crunch through all of the questions on the SAT the normal (i.e., hard) way, you would run out of time. The SAT is deliberately designed to reward you for some advanced reasoning on the math portion instead of brute force.

This article series contains the following articles related to Quick Division on the SAT Test:

• Quick Division on the SAT Test: an introduction
• SAT Test Quick Division Answers

Quick Division on the SAT Test

Learn these tricks and you’ll pick up some valuable time to spend on the harder questions – the questions that get you the extra points other students won’t have time to answer. Plus, these tricks will help you in life to, figuring grocery prices, gas prices, baseball stats and more on the fly. You’ll look like a real math geek – if you’re into that sort of thing.

Here are some tricks for division that are easy to remember from 1-10 

You can divide any whole number by 1.

Even numbers can be divided by 2.

You can divide a number by three if its digits added together are divisible by 3. For example, you can divide 9,213 by 3 because 9 + 2 + 1 + 3 = 15, and 15 ÷ 3 = 5, so you know that 9,213 is divisible by 3.

You can divide a number by 4 if it’s last two digits are divisible by 4. For example, 98,312 is divisible by 4 because 12 is divisible by 4.

Any number that ends in 0 or 5 is divisible by 5.

You can divide a number by 6 if it is even and you can also divide by 3. This sort of makes sense because 6 is 2 x 3. So I remember the rule by applying the 2 rule (is the number even) and then the 3 rule (do the digits add up to a number divisible by 3). For example, 4,212 is even and the digits add up to 9, which is divisible by 3. So it must be divisible by 3.

No rules apply to the number 7, so it is unlikely that the SAT will test divisibility by 7. If it does, perhaps it is really getting at another principle that is less obvious than divisibility.

You can divide a number by 8 if it’s last three digits are divisible by 8. For example, 549, 288 is divisible by 8 because 288 is divisible by 8. This is the hardest rule to put into practice since you will be dividing a three digit number.

You can divide a number by 9 if its digits added together can be divided by 9. I remember this as a variant of the 3 rule. Since 9 is 3 x 3, I use the same rule but with a 9 instead of a 3. For example, 514,872 is divisible by 9 because 5 + 1 + 4 + 8 + 7 + 2 = 27 which is divisible by 9.

Any number that ends in 0 can be divided by 10.

During the process of elimination, it is often a good idea to start with the “2” and “3” rules. Why? Because if a number fails the “2” rule (i.e., the number is odd) it will necessarily fail the “4,” “6,” “8,” an d”10″ rules. And if a number fails the “3” rule, it will necessarily fail the “6” and “9” rules. 

Now let’s get some practice:

1. Which of the following numbers can be evenly divided into 13,548,915,486?

(A) 2
(B) 4
(C) 6
(D) 9
(E) 10

2. A crate has 3,448 bolts. The bolts could be evenly divided into which of the following number of boxes?

(A) 3
(B) 5
(C) 6
(D) 8
(E) 10

3. A box has 63 red blocks, 47 blue blocks and 95 yellow blocks. If you added 1 more of each type of block to the box, each of the three colors of blocks could be evenly divided among a group of children. What is the greatest possible number of children in the group:

(A) 8
(B) 12
(C) 15
(D) 16
(E) 32

Make sure you try to answer the above before moving onto the answer explanations in the next article, SAT Test Quick Division Answers.