In a survey, \$100\$ travel agents every ranked airline \$A\$, \$B\$, and also \$C\$ in stimulate of preference. Every of the \$100\$ travel agents additionally rated the three airlines in five categories top top a range of \$1\$ v \$10\$, with \$10\$ gift the best rating.

You are watching: If each of the average ratings If each of the typical ratings to be the arithmetic mean of the ratings provided by the \$100\$ travel agents, approximately how much better was the total of the ratings given to all 3 airlines for integrity than the for promptness?

\$25\$\$50\$\$125\$\$250\$\$500\$

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## Survey the Question

Let’s search the trouble for clues as to what it will certainly be testing, as this will help transition our minds come think around what form of math knowledge we’ll usage to fix this question. Pay fist to any type of words that sound math-specific and also anything special around what the numbers look like, and also mark castle on ours paper.

We have actually both a pie graph and a table containing numerical data, therefore this question most likely tests what us know about Graphical techniques for relenten Data. Let’s keep what we’ve learned about this ability at the reminder of our minds together we approach this question.

## What do We Know?

Let’s very closely read through the question and make a list of the points that us know.

We desire to calculate the difference in between the full reliability rating because that all 3 airlines combined and the complete promptness rating because that all three airlines combinedThe convenience ratings are provided in a table

## Develop a Plan

The table offers us mean values, yet the question is trying to find a total value, or sum. Thinking of one equation relating the two, us remember that:

\$\$Average = Sum of Values/Number of Values\$\$

Since the inquiry is looking for the amount of the values, let’s resolve for this variable:

\$\$Sum of Values = Average·Number of Values\$\$

Since there are \$100\$ travel agents giving the ratings, the number of values is same to \$100\$. The “Average” that we are searching for is the median difference between reliability and promptness, added together for all 3 airlines. For this reason let’s subtract promptness from dependability for each airline, add these worths together, climate multiply by \$100\$ to transform this average into a sum.

## Solve the Question

We recognize that the linked difference between the promptness and reliability ratings have the right to be uncovered by including together these differences in between each of the three airlines.

\$\$Average Difference = (A_Reliability-A_Promptness)+(B_Reliability-B_Promptness)+(C_Reliability-C_Promptness)\$\$

We can obtain these 6 promptness and reliability averages for airline \$A\$, \$B\$, and also \$C\$ indigenous the table and also simplify the best side of the equation.

 \$Average Difference\$ \$=\$ \$(7.8-6.5)+(7.5-6.9)+(4.9-4.1)\$ \$ \$ \$ \$ \$Average Difference\$ \$=\$ \$1.3+0.6+0.8\$ \$ \$ \$ \$ \$Average Difference\$ \$=\$ \$2.7\$

So because that each travel agent, the amount of the median differences between the promptness and also reliability ratings because that all three airlines combined was \$2.7\$. We can acquire the amount of the average differences by multiplying by the number of travel agents. Doing so, we get \$2.7·100=270\$. Looking for the answer an option closest come \$270\$, we can see that the exactly answer is D, \$250\$.

## What Did us Learn

Though the principle tested in this question wasn’t too complicated by GRE standards, the was absolutely worded in a confound way, wherein we necessary to discover the amount of the typical of the distinction of averages (say that 3 times fast!). We should always slow down and also read these types of inquiries deliberately to minimization the likelihood of wrongly assessing what the concern is asking for.

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