Nichols wrote:

If A and B are consecutive positive integers less than 100, what is the value of B?

1. A is the cube of an integer.

2. B is the square of an integer.

1.) Insufficient, doesn't tell us anything about B.

This statement implies

cube root of A<5. \(5^3=125\), \(4^3=64\).

2.) Insufficient, this statement tells us \(\sqrt{B}<10\).

1&2.) Sufficient. Taken together cube root of A<5 and \(\sqrt{B}<10\) AND consecutive integers, the only values that meet the given conditions are \(A=2^3=8\) and \(B=3^2=9\)