Explanation

The question is simple. We can take note that f must be an integer. On to the statements, separately first.

My normal approach to Statement (1) would be to multiply out the left side, bring over the 10, and solve the quadratic equation by factoring. However, we note that f has to be an integer. The possibility leaps out, since then, , and . However, since this equation is a quadratic in disguise, it may have another solution. The quadratic has two roots, and while those roots could be the same, they are often different. Often the other solution involves flipping a sign. In fact, if , then , and . That's the other possibility. So there are two cases allowed by the data given, and they yield different values of f, so Statement (1) is insufficient.

Statement (2) has a bizarre appearance. Sometimes, GMAT equations or statements are dressed up to be confusing-looking. If we introduce the temporary, intermediate variable, , then we can rewrite the statement in a slightly simpler form:



This means that a certain number g, when taken to the g power, yields 256. We'll understand this by considering cases. What is 2 to the power of 2? It's 2 squared, or 4. What's 3 to the power of 3? Three cubed, or 9 x 3 = 27. Next, 4 to the 4th power is 16 squared.



And that's 256. That means that g is 4, and hence 2f is 4, and hence f=2. The information determines a unique value of f, so Statement (2) is sufficient.

The correct answer is (B).