Batting Average vs. Number of Hits on the GMAT
This tip for improving your GMAT score was provided by David Newland at Veritas Prep.
In the U.S., the baseball playoffs are in full swing. As teams strive to win the World Series, it is a great time to look back at the individual performances of players during the past season. Perhaps the most quoted statistic for each hitter is the “batting average.”
The batting average is simply “the number of hits / the number of at bats.” Basically the batting average is “what is the probability that this player will get a hit on any given at bat?” This statistic is simple, yet powerful in that it allows players to be compared with each other in a meaningful way.
Batting average vs. # of hits
If I told you that a particular player got 100 hits during the baseball season while his teammate got 150 hits, you might be tempted to say that the player with 150 hits was more successful. But what if you learned that the 100 hits came in just 300 at bats (a 1/3 success rate), while it took 600 at bats for the teammate to get his 150 hits (just a 1/4 success rate)?
This is where batting average comes in. Because a batting average is a percentage, it brings its own context, and for this reason batting averages can always be compared. If instead of the number of hits for each player, you were told that their respective batting averages were .333 and .250, you could reasonably conclude that the player with the higher average was generally more likely to get a hit.
Batting average on the GMAT
The GMAT often plays on the difference between an average and an actual number. Take the following example of an official data sufficiency question from the GMATPrep practice tests:
“Warehouse W’s revenue from the sale of sofas was what percent greater this year than it was last year?
(1) Warehouse W sold 10 percent more sofas this year than it did last year.
(2) Warehouse W’s selling price per sofa was $30 greater this year than last year.”
The question asks for a percentage increase in revenue. Since revenue = price per unit x number of units, it is clear that neither statement 1 nor statement 2 is sufficient alone. Statement 1 gives information about the number of units sold, and statement 2 addresses the price per unit. This question requires you to take both statements together to see if you can determine the percentage increase in revenue. The correct answer will therefore be C, “both together are sufficient,” or E, “the statements together are not sufficient to answer the question.”
These two statements provide the two different kinds of information discussed above. Statement 1 provides you with a percentage (like the batting average), while statement 2 provides you with the raw number (like the number of hits).
In most cases, the percentage information is more directly useful for a comparison, while the raw number can be compared only if the appropriate context is provided. For this particular problem, statement 1 allows for a direct comparison between this year and last year, while statement 2 requires a starting number to truly compare the selling price.
Because statement 1 gives you a percentage, the actual number of sofas does not matter for this question. If Warehouse W sold 10 percent more sofas this year than last year, no additional information is needed for the comparison.
Statement 2, however, indicates that the selling price was $30 more this year than last year. To know how this effected the revenue for Warehouse W, you would need to know the actual selling price. A $30 increase on a $100 sofa is quite different from a $30 increase on a $1,000 sofa. For this reason the correct answer is E. You cannot determine the percentage increase in revenue from the information given.
If you want to hit a home run on the GMAT, remember that percentages, like batting averages, are comparable, whereas numbers require context.
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