PP1 (Shorter) Quant Section 1 (Medium) Q8

<p><span style="font-size:20px;"><span style="color:#8e44ad;">Understanding the Problem</span></span></p> <p>What the hell is this problem even asking us? It seems like ETS is using deliberately convoluted language to trip us up. Let&#39;s break it down.</p> <ul> <li><strong>Question:&nbsp;</strong>If each of the average ratings was the arithmetic mean of the ratings given by the $100$ travel agents...</li> <li><strong>Translation:&nbsp;</strong>Let&#39;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 $5.1$.</li> </ul> <p><span style="font-size:20px;"><span style="color:#27ae60;">Solving the Problem</span></span></p> <p>Now that we got that out of the way, let&#39;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&#39;s a total of $100 \times 7.8 = 780$.&nbsp;For Airline B, each of the $100$ agents gave a score of $7.5$. That&#39;s a total of $100 \times 7.5 = 750$.&nbsp;For Airline C, each of the $100$ agents gave a score of $4.9$. That&#39;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:</p> <p style="text-align: center;">$$100(7.8) + 100(7.5) + 100(4.9) = 100(7.8 + 7.5 + 4.9) = 100(20.2) = 2020$$</p> <p>We repeat the process for Promptness for all three airlines:</p> <p style="text-align: center;">$$100(6.5) + 100(6.9) + 100(4.1) = 100(6.5+6.9+4.1) = 100(17.5) = 1750$$</p> <p>Finally, we take the difference between the two: $2$,$020 - 1$,$750 = 270$. Thus, the closest and <strong><span style="color:#27ae60;">correct answer is D ($250$)</span></strong>.</p>