First, rearrange the inequality to better isolate n.

1/(2^n) < 0.005
1 < 0.005(2^n)
1/0.005 < 2^n
1000/5 < 2^n
200 < 2^n

The smallest integer power of 2 that is greater than 200 is 256, which is equal to 2^8. If n is smaller than 8, 2^n is smaller than 200. Choice (A) is correct.