18. How many four-digit numbers $N$ are there, such that half of the number $N$ is divisible by 2 , a third of $N$ is divisible by 3 and a fifth of $N$ is divisible by 5 ?
A 1
B 7
C 9
D 10
E 11
SolUtion
D

The information in the question tells us that $N$ is divisible by $2 \times 2=4,3 \times 3=9$ and $5 \times 5=25$. Since these three values have no factors in common, $N$ is divisible by $4 \times 9 \times 25=900$. Therefore $N$ is a four-digit multiple of 900 . The smallest such multiple is $2 \times 900=1800$ and the largest is $11 \times 900=9900$. Therefore there are 10 such four-digit numbers.