Mastering Divisibility: Understanding the Rule for 4

What is the rule for checking if a number is divisible by 4?

• A. The number should end in an even digit
• B. The number formed by the last two digits must be divisible by 4
• C. The sum of the digits must be even
• D. The greatest digit must be 4

Answer: (B)

For a number to be divisible by 4, the correct method involves looking specifically at the last two digits of the number. This is because a number is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, in the number 536, the last two digits are 36. Since 36 can be divided by 4 evenly (36 ÷ 4 = 9), we can determine that 536 is divisible by 4. This two-digit rule works because of how numbers are structured; every four numbers (e.g., 00, 04, 08, etc.) repeat the divisibility pattern. Thus, even if the preceding digits are not divisible by 4, as long as those last two digits are, the entire number will be divisible by 4 as well. Other options do not accurately reflect the rule for divisibility by 4. Checking if the entire number ends in an even digit, whether the sum of the digits is even, or if the greatest digit is 4 does not guarantee divisibility by 4 in all cases.

When it comes to numbers and their quirks, understanding divisibility rules is like having a secret code to unlock math problems. And if you've been scratching your head about the divisibility rule for 4, you're in for a fun learning ride! So, let’s break it down together.

What’s the Rule, Anyway?

Here’s the scoop: to check if a number is divisible by 4, all you have to do is focus on the last two digits of that number. Yup, you read that right! Just the last two will do. So, in a number like 536, the last two digits are 36. If 36 can be divided by 4 without a remainder, then the whole number—536 in this case—is divisible by 4.

But why does this work? It’s all about how numbers are structured. Picture counting in groups of four: 00, 04, 08, 12, and so on. This distinct pattern means that every single four-number cycle resets the divisibility rule. Clever, huh?

Let’s Crunch Some Numbers

Okay, let’s put this rule to the test! Take a number like 812. What are the last two digits? That's right, 12! Now perform a quick check: 12 ÷ 4 equals 3. Since there's no remainder, 812 is divisible by 4. Easy peasy!

Now, you might wonder, "What about those other options I came across?" Let’s quickly squash those misconceptions:

• Ending in an Even Digit: Just because a number ends in 2, 4, 6, 8, or 0 doesn’t guarantee it’s divisible by 4. Take 12 for instance; it works, but what about 22? It's even but not divisible by 4.

• The Sum of the Digits Must Be Even: While cool for some other math tricks, this doesn’t indicate divisibility by 4.

• The Greatest Digit Must Be 4: This is a misleading notion. The largest digit can be anything and still not make a number divisible by 4.

Why Does It Matter?

So why get cozy with this rule, especially if you're prepping for the GMAT? Well, time is of the essence, especially on standardized tests. Knowing tricks like these helps you answer questions quickly and effectively, meaning you’ve got more time left in your exam to tackle the tougher problems. And hey, who doesn’t want to breeze through the math section?

A Little Extra Insight

Numbers can dance in mysterious ways. It’s fascinating to realize that something as simple as the last two digits can decide whether you're on the right track or not. So, the next time you encounter a number and want to know if it’s divisible by 4, remember this little trick—it’s like having a secret weapon in your math arsenal!

Wrap-Up

Before you go, keep this golden rule close to your heart: check those last two digits! You’re now one step closer to mastering math challenges and, ultimately, acing that GMAT. Who knew numbers could be this much fun? Happy calculating!