Explanation

The right side of the inequality given here is , half a quarter, so we are being asked whether the following is true:



The left side of this thing will equal the right side when . For higher values of k, the left side will only get tinier and tinier, as the denominator gets bigger and bigger; indeed, any fraction less than 1 becomes smaller when taken to a positive exponent. That means that the answer to the question here will be "no" when , and "yes" when . Let's go to the statements, separately first.

Statement (1) tells us that . Therefore, we have sufficient information to answer the question definitively, in the negative, so Statement (1) is sufficient.

Statement (2) can be manipulated to be directly comparable to the question at hand:









In the last step on the left side, recall that exponents simply count how many times something is multiplied; with another , the count increases by 1 from k-1 to k. We now have a statement that is identical to what we wanted to know, but the sign of the inequality is flipped. Therefore, the answer to the question posed is a decisive "no," based on Statement (2). Statement (2) is therefore sufficient.

The correct answer is (D).