How many numbers between 1 and 300 are divisible by 3 and 5 but not by 7?
Answer: B
A number divisible by 3 and 5 is divisible by their LCM, which is 15. The number of multiples of 15 up to 300 is \(\lfloor 300/15 \rfloor = 20\). Now we need to subtract the numbers that are also divisible by 7. A number divisible by 15 and 7 is divisible by their LCM, which is 105. The number of multiples of 105 up to 300 are \(\lfloor 300/105 \rfloor = 2\) (which are 105 and 210). So, the required number of numbers is \(20 - 2 = 18\).