The Department of Environmental Protection measured the volume of wate

Official solution provided by Veritas prep

This difficult data sufficiency question tests an important number property relating to standard deviation: if the terms in a set are each decreased by a fixed percentage, then the standard deviation decreases by that same percentage (unless the terms are all the same to begin with – then the standard deviation would be zero before the change and zero after). In the question stem you learn that the standard deviation of 10 measurements is 4 million at the beginning of the year (note – this guarantees that they are not all the same), and you must decide if that standard deviation had decreased at the end of the year. In statement (1) you learn that the average volume of the 10 reservoirs decreased by 20% over the year. Importantly this does NOT mean that each term decreased by 20%. A decrease in the average of all 10 volumes might yield a smaller standard deviation, but it could easily result in a larger standard deviation. Consider a sample set of 5, 10, and 15, which has an approximate standard deviation of 4. If the average of those 3 numbers is decreased by 20%, then the new set could be 5, 4, and 15 (average went from 10 to 8) and this set clearly has a higher standard deviation just by inspection (approximately 5 if you do the calculation). Remember that you do not need to calculate the standard deviation – just realize that you do not know how the set was changed to decrease the average, so you do not know the effect on the standard deviation. Statement (1) is not sufficient. With statement (2) you must be very careful as it appears to give you the information that was lacking in statement (1): it proves that each one had the same percentage decrease. At this point, many students will pick (C) as they fit together so nicely. However statement (2) is actually sufficient by itself: if the volume of each reservoir decreased by the same percentage (and the volume for each was not the same to begin with – something you know from the question stem) then the standard deviation MUST be lower after that change. It guarantees that the set “shrunk” during the year, reducing the dispersion and thus the standard deviation. Answer is B – statement 2 alone is sufficient.