Let's start with a simpler scenario. If you made $1,000 in sales, we'd find the average value of your transactions by dividing that total by the number of transactions. So if you had 10 transactions, the average would be $100, but if you had 50 transactions, the average would be $20, right?

Here, we aren't told the number of transactions, but we're told the

proportion of transactions in each region. So if Techtyx had 100 transactions, 5 of them would have been in E and 33 would have been in C. We can use a Smart Number like this, or we can simply divide by the original (decimal) proportion. We'll get different numbers with those two different approaches, but the

relative values for the different regions will stay the same. So if we estimate that E had sales of $750K and C had sales of $800K, their averages per transaction would be $800K/33 and $750/5 (if we plug in #s) or $800K/.33 and $750K/.05 (if we use the decimals). In either case, E's number is much bigger than C's (and all the rest). We can see this quickly by noting that E's sales are among the highest, while its number of transactions is the lowest. Since none of the other regions have a lower denominator (fewer transactions), we just have to compare to the two regions (C and F) that have higher numerators (higher $ sales). F has 3 times as many transactions as E. To match E's average, F would have to have sales around $2,250K. C would have to have over 6 times E's sales, or over $4,500K.!

Let me know if that helps.

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Dmitry Farber | Manhattan GMAT Instructor | New York

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