if P represents the number of prime numbers between 1 and 102 then wha

Dear stonecold,
I'm happy to respond.

My friend, where on earth did you get this question? This is, in many ways, a tedious counting question in which we just have to list out the individual cases. It helps, of course, to be conversant in the primes from one to 100. There's really no other way to answer this besides listing all the examples. This is not particularly GMAT-like: I am not familiar with any GMAT question which cannot be solved in any shortcut way and which requires writing out a tedious list.

Here's the list, grouped in sets of five for easy counting
2--3--5--7--11
13--17--19--23--29
31--37--41--43--47
53--59--61--67--71
73--79--83--89--97
101

That's 26 prime numbers. Answer = (B)

Incidentally, it's helpful to note that {101, 103, 107, 109} are all prime. In other words, all the odds except the multiple of 5 are prime between 100 and 110, as is true between 10 and 20. This is also true between 190 and 200.

Does all this make sense?
Mike