How many 2-digit or 3-digit numbers can be formed using the digits 134568 and 9 which are diisible by 4?

Answer 1

48.

Assuming no digit can be used more than once, the two digit numbers divisible by 4 are:

16, 36, 48, 56, 64, 68, 84, 96

8 of them.

For any number to be divisible by 4, only the last two digits need be divisible by 4; so for three digit numbers, each of the two digit numbers above can be preceded by any of the remaining 5 digits and still be divisible by 4.

→ 5 x 8 = 40 three digit numbers are divisible by 4

→ 40 + 8 = 48 two or three digit numbers made up of the digits {1, 3, 4, 5, 6, 8, 9} are divisible by 4.

If repeats are allowed, there are an extra 2 two digit numbers (44 and 88) and each of the two digit numbers can be preceded by any of the 7 digits, making a total of 7 x 10 + 10 = 80 two and three digits numbers divisible by 4 make up of digits from the given set.