The tens digit is a multiple of 5
The hundreds digit is 1 less than the tens digit
The ones digit is less than the hundreds digit
The sum of the digits is a multiple of 6
What is the mystery number??
_ _ _
Tens digit:
_ 5 _
Hundreds digit:
4 5 _
Ones digit must be 0, 1, 2, or 3
4 5 ?
Take it from there.
453
Let's break down the given information to find the mystery number step-by-step:
Step 1: The tens digit is a multiple of 5.
From this information, we can conclude that the tens digit could be either 0 or 5.
Step 2: The hundreds digit is 1 less than the tens digit.
Since the tens digit could be either 0 or 5, the hundreds digit could be either -1 or 4.
Step 3: The ones digit is less than the hundreds digit.
This information tells us that the ones digit must be less than either -1 or 4, which means it could be either 0, 1, 2, or 3.
Step 4: The sum of the digits is a multiple of 6.
To satisfy this condition, we need to find a combination of the tens, hundreds, and ones digits that adds up to a multiple of 6.
Now let's try out the possible combinations:
Combination 1: Tens digit = 0, Hundreds digit = -1, Ones digit = 0
In this case, the sum of the digits is 0 + (-1) + 0 = -1, which is not a multiple of 6.
Combination 2: Tens digit = 0, Hundreds digit = -1, Ones digit = 1
In this case, the sum of the digits is 0 + (-1) + 1 = 0, which is a multiple of 6.
Combination 3: Tens digit = 5, Hundreds digit = 4, Ones digit = 0
In this case, the sum of the digits is 5 + 4 + 0 = 9, which is not a multiple of 6.
Combination 4: Tens digit = 5, Hundreds digit = 4, Ones digit = 1
In this case, the sum of the digits is 5 + 4 + 1 = 10, which is a multiple of 6.
Therefore, the only combination that satisfies all the given conditions is when the mystery number is 510.
To find the mystery number, we can follow these steps:
Step 1: Start with the information given:
- The tens digit is a multiple of 5.
- The hundreds digit is 1 less than the tens digit.
- The ones digit is less than the hundreds digit.
- The sum of the digits is a multiple of 6.
Step 2: Let's use some logical deduction to narrow down the possibilities based on the given information.
From the first statement, we know that the tens digit must be either 0 or 5 since these are the only multiples of 5.
Next, from the second statement, we can deduce that if the tens digit is 0, then the hundreds digit would be -1, which is not possible for a digit. Therefore, we conclude that the tens digit must be 5.
Now, since the hundreds digit is 1 less than the tens digit, it has to be 4.
Moving on to the third statement, which says that the ones digit is less than the hundreds digit. The only possible digit smaller than 4 is 3.
Finally, we need to check if the sum of the digits is a multiple of 6. The sum of 5, 4, and 3 is 12, which is indeed divisible by 6.
Therefore, the mystery number that satisfies all the given conditions is 543.