Trouser Price Puzzle: Divisibility By 2, 3, And 5!

by TextBrain Team 51 views

Let's dive into a fun little math problem, guys! We've got a pair of trousers, and we need to figure out which of the given prices can't be the real price based on whether the price is divisible by 2, 3, and 5. Sounds like a cool detective game, right? So, let's put on our thinking caps and get started!

Understanding Divisibility Rules

Before we jump into analyzing the options, let's quickly refresh our memory on divisibility rules. These rules will be our secret weapons in cracking this puzzle!

  • Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
  • Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
  • Divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5.

Now that we have these rules in our arsenal, we can efficiently check each of the given options to see if they fit the divisibility criteria mentioned in the problem. Remember, the key is to find the price that doesn't work with the given information. Keep these rules handy, because we're about to put them to the test!

Let's keep these divisibility rules in mind as we break down each option. This will help us figure out which trouser price just doesn't fit the mold. It's like being a math detective – super fun and engaging!

Analyzing the Options

Okay, now let's roll up our sleeves and examine each of the price options to see which one doesn't play nice with the divisibility rules. We'll go through each one step-by-step.

A) 250 TL

Let’s consider 250 TL first. To check if 250 is divisible by 2, 3, and 5, we apply the divisibility rules:

  • Divisibility by 2: The last digit of 250 is 0, which is even. Therefore, 250 is divisible by 2.
  • Divisibility by 3: The sum of the digits of 250 is 2 + 5 + 0 = 7, which is not divisible by 3. Therefore, 250 is not divisible by 3.
  • Divisibility by 5: The last digit of 250 is 0, so 250 is divisible by 5.

So, 250 is divisible by 2 and 5, but not by 3. This option could be a potential answer, but let's keep it in mind as we check the other options.

B) 370 TL

Now, let’s evaluate 370 TL. Again, we will use our divisibility rules:

  • Divisibility by 2: The last digit of 370 is 0, which is even. Thus, 370 is divisible by 2.
  • Divisibility by 3: The sum of the digits of 370 is 3 + 7 + 0 = 10, which is not divisible by 3. Thus, 370 is not divisible by 3.
  • Divisibility by 5: The last digit of 370 is 0, indicating that 370 is divisible by 5.

So, just like 250, the number 370 is divisible by 2 and 5, but not by 3. This could also be a possible answer. Let’s move on to the next one.

C) 440 TL

Let's take a look at 440 TL. Time to put those divisibility rules to work again!

  • Divisibility by 2: The last digit of 440 is 0, meaning it's divisible by 2.
  • Divisibility by 3: The sum of the digits is 4 + 4 + 0 = 8, which is not divisible by 3. So, 440 is not divisible by 3.
  • Divisibility by 5: The last digit is 0, so 440 is divisible by 5.

Just like the previous options, 440 is divisible by 2 and 5 but not by 3. This could also potentially be the answer we're looking for!

D) 480 TL

Finally, let's investigate 480 TL. We'll use our trusty divisibility rules:

  • Divisibility by 2: The last digit of 480 is 0, so it is divisible by 2.
  • Divisibility by 3: The sum of the digits is 4 + 8 + 0 = 12, which is divisible by 3. So, 480 is divisible by 3.
  • Divisibility by 5: The last digit of 480 is 0, meaning it is divisible by 5.

Here’s the key difference: 480 is divisible by 2, 3, and 5. This means that if the problem states the price is not divisible by one of these numbers, then 480 can't be the answer.

Determining the Correct Answer

Alright, guys, we've done the detective work and analyzed each option! Now, let's pinpoint which price cannot be the price of the trousers.

We are looking for a number that doesn't fit a specific divisibility criterion. From our analysis:

  • 250 is divisible by 2 and 5, but not 3.
  • 370 is divisible by 2 and 5, but not 3.
  • 440 is divisible by 2 and 5, but not 3.
  • 480 is divisible by 2, 3, and 5.

Since the question implies that the price is not divisible by at least one of the numbers (2, 3, or 5), the number that is divisible by all three (2, 3, and 5) cannot be the price. Therefore, the answer is D) 480.

So, there you have it! We solved the trouser price puzzle using divisibility rules. It's all about understanding the properties of numbers and applying them logically. Great job, everyone!

Conclusion

In conclusion, understanding divisibility rules can make solving math problems much easier and faster. By systematically checking each option against the divisibility rules for 2, 3, and 5, we were able to determine that 480 TL could not be the price of the trousers, based on the given conditions. These rules aren't just useful for puzzles; they can also help in everyday calculations and problem-solving scenarios. Remember, math can be fun and engaging when approached with the right tools and strategies!