Call a number Guardian if it is composite but not divisible by 2, 3, or 5. The three smallest guardian numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many Guardian numbers are there less than 1000?
Select:
A) 100	B) 102	C) 104	D) 106	E) 108
S1 = total number of numbers divisible by 2 from 1-1000 = 500   S2 = total number of numbers divisible by 3 from 1-1000 = 333   S3 = total number of numbers divisible by 5 from 1-1000 = 200   S4 = total number of numbers divisible by 2 and 3 = 166   S5 = total number of numbers divisible by 2 and 5 = 100   S6= total number of numbers divisible by 3 and 5 =66   S7 = total number of numbers divisible by 2,3 and 5 = 33   thus total number of numbers divisible by 2,3 or 5 are = 500 +333+200-166-100-66+33= 
<gadget id="calculator">500 +333+200-166-100-66+33</gadget>
<output>734</output>
734   now since we have already included 2,3 and 5 while calculating their multiple in the above calculations, hence total number of prime numbers from 1-1000 becomes= 168-3= 
<gadget id="calculator">168-3</gadget>
<output>165</output>
165   also, since 1 is neither composite nor prime, hence we will subtract 1 from the final answer.   thus total number of guardian numbers are 1000-734-1-165= 
<gadget id="calculator">1000-734-1-165</gadget>
<output>100</output>
100   100NSWER:100
<result>A</result>
Call a number Guardian if it is composite but not divisible by 2, 3, or 5. The three smallest guardian numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many Guardian numbers are there less than 1000?