A5. How many five-digit numbers (such as 12345 or 78000; the first digit is never 0) are there that end in a 4 and are divisible by 6?
A) 1500
B) 2000
C) 3000
D) 7500
E) 8998
A5. C) 3000 If $x$ is a positive multiple of 6 that ends in a 4 (such as 24), then the next multiples of 6 end in a $0(x+6)$, a $6(x+12)$, a $2(x+18)$, an 8 $(x+24)$, a $4(x+30)$, so the next multiple of 6 that ends in a 4 is $x+30$. Therefore, in every group of thirty consecutive numbers, there is exactly one multiple of 6 that ends in a 4. How many such numbers are there between 10000 and 99999? Since there are a total of 90000 consecutive numbers, we find that among these numbers, $90000 \div 30=3000$ such multiples of six ending in a 4.