Three options for the last two digits (00, 24, 48). For the first digit, 4 options. For the rest, 7 options each. Total: 84 numbers.
To form a six-digit number greater than 500,000 and divisible by 4 using the given digits (0, 1, 2, 4, 5, 7, 8, 9), we can follow the hint provided.
A number is divisible by 4 if its last two digits are divisible by 4.
Considering the last two digits, we have the options 00, 12, 24, 48, 52, 72, 84, 92.
Out of these, 00, 24, and 48 are divisible by 4. Now, we need to consider the remaining four digits.
For the first digit (hundred thousands place), we can use any of the digits 5, 7, 8, or 9, since the number needs to be greater than 500,000.
For the remaining three digits (ten thousands, thousands, and hundreds places), we have seven digits to choose from (0, 1, 2, 4, 5, 7, 8, 9).
So, the total number of six-digit numbers greater than 500,000 and divisible by 4 is calculated by multiplying the possibilities for each place:
3 (choices for the last two digits) * 4 (choices for the hundred thousands place) * 7 (choices for the remaining three digits) = 84.
Therefore, 84 six-digit numbers satisfying the given conditions can be formed using the specified digits.
Question
"How many six-digit numbers greater than 500,000 and divisible by 4 can be formed using the digits 0, 1, 2, 4, 5, 7, 8, 9. These numbers can be used repeatedly.(Hint: If the last two digits are divisible by 4, the whole number is divisible by 4.)