How many positive integers, from 2 to 100, inclusive, are no

Hi,

This question is based on a subtle Number Property rule. If you don't immediate recognize the NP rule, then that's okay, but you'll have to do some work to discover that 'pattern' involved....

We're asked to think about the numbers 2 to 100, inclusive. To start, there's NO way that the GMAT would ask us to truly think about each of these numbers individually, so you should be thinking that there's a pattern involved.

Now to the specifics: which of these numbers are NOT divisible by an odd integer that is greater than 1???

Let's start at the first number and work our way "up" until the pattern becomes clear:

2 - this is NOT divisible by any odd integers, so this "fits" what we're looking for...
3 - this IS divisible by an odd integer (3), so it's out
4 - this is NOT divisible by any odd integers, so this "fits"
5 - this IS divisible by an odd integer (5), so it's out
6 - this IS divisible by an odd integer (3), so it's out
7 - this IS divisible by an odd integer (7), so it's out
8 - this is NOT divisible by any odd integers, so this "fits"

Now, looking at the numbers that "fit", we have 2, 4 and 8.....that's 2^1, 2^2 and 2^3....that MUST be the pattern involved, so we can use this against the rest of the question to find the other values that "fit":
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128, but that's outside the range that we were given. Thus, there are 6 values that "fit" what we're looking for.

Final Answer:

GMAT assassins aren't born, they're made,
Rich