If P is a positive integer such that 3P is divisible by 5 and 7P is divisible by 11, what is the smallest possible value of P?

✓ Correct Answer: Option B

For 3P to be divisible by 5, P must be a multiple of 5. For 7P to be divisible by 11, P must be a multiple of 11. Thus, P must be a multiple of both 5 and 11. The smallest such positive integer is their LCM, which is 5 * 11 = 55.