Plane X flies at r miles per hour from A to B. Plane Y flies at S miles per hour from B to A. Both planes take off at the same time. Which plane flies at a faster rate? Town C is between A and B.
(1) C is closer to A than it is to B.
(2) Plane X flies over C before plane Y
Given:Plane X - A to B (Speed: r miles per hour)
Plane Y - B to A (Speed: s miles per hour)
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: C is closer to A than it is to B.
This statement tells us about the distance only, but we cannot infer anything about which plane reaches C first. Hence, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Plane X flies over C before plane Y
It is given that both planes start at the same time and move towards each other. Now, as this statement tells us that Plane X flies over C before plane Y, Plane X should be faster than Y as Plane X covers a shorter distance to C as C is between A and B, and even so, it reaches before Plane Y.
Thus, r > s for sure.
Hence, Statement 2 is sufficient alone, and so, the correct answer is
Option B - Statement 2 alone is sufficient.
Hope this helps!