How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 6?
Choose the correct answer:
A) 5  B) 6  C) 7  D) 8  E) 9
6   To be divisible by six the sum of the digits must be divisible by 3 and be even. Use same logic as finding all divisible by three but strike all odd answers. Highest number becomes 72 and we select from the divisible by 3 answers the even numbers.   72 -yes   54 -yes   42 - yes   36 - yes   24 - yes   12 - yes   Correct answer is 6.
<result>B</result>
How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 6?