How many five digit numbers can be formed using every digit of 5, 6, 7, 8 and 9 which are divisible by 4?Options36181224
Question
How many five digit numbers can be formed using every digit of 5, 6, 7, 8 and 9 which are divisible by 4?
Options:
- 36
- 181
- 224
Solution
The divisibility rule of 4 is that if the number formed by the last two digits of a number is divisible by 4, then the number is divisible by 4.
The two-digit numbers that can be formed using 5, 6, 7, 8, 9 and are divisible by 4 are: 56, 64, 68, 76, 84, 92.
So, the last two places can be filled in 6 ways.
The remaining three places can be filled in 3! = 321 = 6 ways.
Therefore, the total number of five digit numbers that can be formed is 6*6 = 36.
So, the correct option is 36.
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