Call a number “prime looking” if it is composite but not divisible by 2,3,or 5.  The three 
smallest prime looking numbers are 49, 77 and 91.  There are 168 prime numbers less than 1000.  If  K is number of prime looking numbers less than 1000 then$\frac{K}{200}=$  ______

To find “prime looking numbers” we can apply complementary counting.
We can split the number from 1 to 1000 into following groups
$\left\{1\right\}$, {numbers divisible by 2= $S_2$}, {numbers divisible by 3= $S_3$}, {numbers divisible by 5= $S_5$},{primes not including 2,3,5}, {prime looking numbers}
Hence prime looking numbers =1000-(168-3)-1- $|S_2\cup S_3\cup S_5|$
     =1000-165-1-{500+333+200-166-66-100+33}=100