Understanding the Problem

What the hell is this problem even asking us? It seems like ETS is using deliberately convoluted language to trip us up. Let's break it down.

Question: If each of the average ratings was the arithmetic mean of the ratings given by the $100$ travel agents...
Translation: Let's just assume that each agent gave the same score for each category and airline. For example, for the Convenience of Airline A, assume that each of the $100$ agents gave a score of $5.1$.

Solving the Problem

Now that we got that out of the way, let's solve the problem. We first need to calculate the total score given to all three airlines for Reliability. For Airline A, each of the $100$ agents gave a score of $7.8$. That's a total of $100 \times 7.8 = 780$. For Airline B, each of the $100$ agents gave a score of $7.5$. That's a total of $100 \times 7.5 = 750$. For Airline C, each of the $100$ agents gave a score of $4.9$. That's a total of $100 \times 4.9 = 490$. We then add these three values together to get the total sum. This can be more easily represented by the equation below:

$$100(7.8) + 100(7.5) + 100(4.9) = 100(7.8 + 7.5 + 4.9) = 100(20.2) = 2020$$

We repeat the process for Promptness for all three airlines:

$$100(6.5) + 100(6.9) + 100(4.1) = 100(6.5+6.9+4.1) = 100(17.5) = 1750$$

Finally, we take the difference between the two: $2$,$020 - 1$,$750 = 270$. Thus, the closest and correct answer is D ($250$).