How many four digit numbers that are divisible by 4 can be formed usin

In order for a number to be divisible by 4, the last two digits of the number must be divisible by 4. Since we can choose only digits 0 to 7 and no digits can repeat, the last two digits of the number must be 04, 12, 16, 20, 24, 32, 36, 40, 52, 56, 60, 64, 72 or 76. Let’s separate these numbers into two groups - those with the digit 0 and those without the digit 0.

With the digit 0: 04, 20, 40, 60
Since these are the last two digits of the number, there are 6 choices for the first digit and 5 choices for the second digit. Therefore, there are 6 x 5 x 4 = 120 such numbers if the last two digits have the digit 0.

Without the digit 0: 12, 16, 24, 32, 36, 52, 56, 64, 72, 76

Since these are the last two digits of the number and the first digit of the number can’t be 0, there are 5 choices for the first digit and 5 choices for the second digit. Therefore, there are 5 x 5 x 10 = 250 such numbers if the last two digits do not have the digit 0.

Therefore, there are a total of 120 + 250 = 370 such numbers.

Answer: C