John Bob wants to leave behind his life-time savings of s dollars...

Interesting problem. It's a little bit wordier, for a divisibility problem, than you'd normally see, but it also has kind of a clever trick to it!

JB has a round number of dollars (presumably - this problem should have clearly stated that s is an integer, but let's assume that's what the writer intended.) Since he has s dollars, he has 100s cents. These 100s cents can only be divided among his children if 100s is evenly divisible by c. So, rephrase the question: is 100s divisible by c?

Statement 1: This is a complicated way of saying that c equals either 2 or 4, since those are the only powers of 2 that are between 1 and 8. If c = 2, then 100s/c = 100s/2 = 50s, which is an integer number of cents, so the answer to the question is 'yes'.

If c = 4, the situation is similar. 100s/c = 100s/4 = 25s, which is an integer number of cents, and the answer is "yes" again. So, statement 1 is sufficient.

Statement 2: JB has between 31 and 43 dollars, exclusive. To show that this is insufficient, we should come up with one scenario where his money can't be divided among his (unknown number of) children, and one scenario where it can.

For instance, suppose he has 32 dollars. If he has 7 children (c = 7), then the money can't be evenly divided, since 3200 isn't divisible by 7. But if he has 2 children (c = 2), then the money can be evenly divided, with 16 dollars (1600 cents) going to each child. Since the answer might be yes or no, the statement is insufficient.

So, the answer to the problem is A.

Thank you, ccooley! That's very helpful.