I am a three-digit number. I am divisible by 6. My middle digit is a prime number. The sum of my digit is 9. I am between 400 and 500. My digits are descending order. What number am I?
"I am between 400 and 500"
---> 4XX
"My middle digit is a prime number"
---> 42X 43X 45X 47X
"My digits are descending order"
---> 43X 42X
"The sum of my digit is 9"
---> 432
"I am divisible by 6"
Yup, redundant information.
432 is your number
Thx
Thanks my math teacher put this on a online home work and I got it right so thanks 🥺🥺🥺
Thx so much for this! I needed it for homework and it helped me sooo much!
Thanks again,
Patrick-star
To solve this problem, we need to break it down into smaller steps and find a number that satisfies all the given conditions.
1. The number is divisible by 6: A number is divisible by 6 if it is divisible by both 2 and 3. Since the number has a descending order, the last digit must be an even number, which means it is divisible by 2. Therefore, we need to check if it is divisible by 3.
2. The middle digit is a prime number: Prime numbers are numbers that are only divisible by 1 and themselves. The possible prime numbers in the given range are 2, 3, 5, and 7. Since the digits are in descending order, the middle digit must be larger than the last digit. Hence, the middle digit can only be 5 or 7.
3. The sum of the digits is 9: The sum of the three digits should be 9. Since the digits are in descending order and the last digit is even, the possibilities for the sum are: 4+3+2, 4+3+1, 4+2+1, and 3+2+1.
4. The number is between 400 and 500: As mentioned, the number is between 400 and 500. Therefore, the digit in the hundreds place must be 4.
Now, let's combine all the given conditions:
- The middle digit is a prime number (5 or 7).
- The sum of the digits is 9.
- The digit in the hundreds place is 4.
- The number is divisible by 6.
After checking all the possibilities, we find that the number which satisfies all these conditions is 432.
Therefore, the number you are is 432.