dvalenz wrote:How many 3 digit integers are divisible by 3 and 4?

As Mitch has demonstrated, the fastest approach is to first estimate the answer, and then check whether only one answer choice works.

As Mo has demonstrated, you can also apply the formula for an arithmetic sequences.

If you're not into memorizing formulas, you might also consider this approach:

We're looking for 3-digit multiples of 12. So, let's list a few: 108, 120, 132, . . . 984, 996
So, how many number are in that list?
To find out, let's rewrite each value as a multiple of 12.

108 = (9)(12)
120 = (10)(12)
132 = (11)(12)
.
.
.
984 = (82)(12)
996 = (83)(12)

At this point, we can see that we need only determine the number of integers from 9 to 83 inclusive. To do so, we'll apply an easy-to-remember rule:

The number of integers from x to y inclusive equals y - x + 1

So, the number of integers from 9 to 83 inclusive = 83 - 9 + 1 = 75

Answer = A

Cheers,
Brent