Explanation

This question involves speed, distance and time. We might be able to analyze it with algebra, with analysis by cases, or something more like mental math based on our common experiences. We are asked whether . On to the statements, separately first.

Statement (1) says that . That contributes toward establishing , since it establishes one factor on the left as bigger than a factor on the right, but it's not decisive. We can analyze by cases. Case I: . In this case, it's true that . Case II: a is much smaller than b: . Then, it can be false that . Therefore, we don't have enough information to answer the question decisively, in the affirmative or the negative. Statement (1) is insufficient.

Statement (2) is insufficient for the exact same reasons as Statement (1). The only difference is that now we know about a and b, and we can test cases that involve t and s. Insufficient.

Combined, the statements are more promising. Conceptually, since each term on the left is bigger than a corresponding term on the right, the left must be bigger. We can get more precise by substituting what Statements (1) and (2) tell us into our original inequality:



And if that's not convincing enough, we can go further by multiplying out the left side:





Since s and b are positive, this last inequality will always be true and therefore the answer to the question posed will be definitively "yes." The correct answer is (C).

Here's a variation to explore: if the sign of one of the inequalities had been flipped, the correct answer would be (E), as can be established through analysis by cases similar to what we did for Statement (1).

Again, in this question, the correct answer is (C).