Understanding Divisibility by 11: A Guide for 3-Digit Numbers

When you're tackling the Graduate Management Admission Test (GMAT), there's a high chance you'll come across questions that involve divisibility rules. One such rule that often catches students off guard is divisibility by 11. It might sound complicated, but once you understand how the digits of a number interact, it can become a straightforward aspect of your math toolbox.

What's the Rule Again?

You know what? Divisibility rules can feel like secret codes sometimes, but let's break this one down. For any 3-digit number represented as ABC (where A is the hundreds digit, B is the tens digit, and C is the units digit), the rule states that the difference between the sum of the digits in the odd positions (A and C) and the sum of the digit in the even position (B) should either be 0 or a multiple of 11. In simpler terms, it's all about how A and C relate to B.

So here’s the thing: to put this into action, you calculate (A + C) - B. If that equals 0 or a multiple of 11, you’ve hit the jackpot—you’ve found a number divisible by 11!

Breaking It Down

Let’s illustrate this with an example. Say we have a 3-digit number like 352. Here, A = 3, B = 5, and C = 2. Now plug these into our formula:
(3 + 2) - 5 = 0.

Since our end result is 0, guess what? That means 352 is divisible by 11! Isn’t that neat?

Why Does This Matter?

Now, you might be asking, “Why should I care?” If you're studying for the GMAT, this rule can save you precious time on quantitative reasoning questions. Knowing how to quickly assess whether a number meets the divisibility rule not only helps in solving problems but also builds your confidence. And let’s face it—feeling confident while you’re tackling complex math is half the battle.

Here’s something to ponder: when you're faced with those ticking clocks and high-pressure questions during the GMAT, wouldn’t it be great to have a set of strategies at your fingertips? Absolutely!

Connecting the Dots

It's helpful to remember that this divisibility rule makes connections between the digits of a number. If you find yourself staring down numbers and their digits, try picturing them as little puzzle pieces that fit together only in certain ways. For the rule we've explored here, if A plus C equals B, or if performing our formula results in 0 or a multiple of 11, then you're golden!

In Closing

As you refine your skills and your study strategies, don't forget to utilize these mathematical treasures hidden in the rules of divisibility. By understanding the relationships between the digits, you can boost your performance on the GMAT while also impressing yourself with your newfound knowledge.

So next time you encounter a tricky 3-digit number on your GMAT practice test, take a deep breath—you’re now equipped to tackle it with the flair of a math ninja! Keep practicing, stay curious, and watch those numbers become less daunting one rule at a time.