a 2 digit number, divisable by 6, the 10s unit is 1/2 of the digit unit
12, 24, 36, 48, 60, 66, 72, 78, 84, 90, 96
Which of those numbers meet the other criteria?
no other criteria was given
"the 10s unit is 1/2 of the digit unit"
To find a two-digit number that is divisible by 6, you need to find a number that is both divisible by 2 and 3. Since every number divisible by 6 is also divisible by 2 and 3, we can focus on finding a number that is divisible by 2.
Given that the tens digit is half of the units digit, let's represent the tens digit as x and the units digit as 2x. To create a two-digit number, both the tens and units digits must be non-zero, meaning x cannot be 0.
Since we know that the number is divisible by 2, the units digit (2x) must be an even number (ending with 0, 2, 4, 6, or 8). Therefore, x can only be one of the numbers {1, 2, 3, 4, 5}.
To find the valid values for x, we need to check each one of them and see which one satisfies the condition that the number is divisible by 3. For a number to be divisible by 3, the sum of its digits must be divisible by 3.
Let's go through the possible values of x:
For x = 1, the units digit is 2x = 2, and the sum of digits is 1 + 2 = 3. Since 3 is divisible by 3, the number formed is 12, which is divisible by 6.
For x = 2, the units digit is 2x = 4, and the sum of digits is 2 + 4 = 6. Since 6 is divisible by 3, the number formed is 24, which is divisible by 6.
For x = 3, the units digit is 2x = 6, and the sum of digits is 3 + 6 = 9. Since 9 is divisible by 3, the number formed is 36, which is divisible by 6.
For x = 4, the units digit is 2x = 8, and the sum of digits is 4 + 8 = 12. Since 12 is divisible by 3, the number formed is 48, which is divisible by 6.
For x = 5, the units digit is 2x = 10, and the sum of digits is 5 + 10 = 15. Since 15 is divisible by 3, the number formed is 510, which is divisible by 6.
Therefore, the possible two-digit numbers that satisfy the given conditions are 12, 24, 36, 48, and 510.