Looking at statement (2) first, we see that it is not sufficient, because the average (arithmetic mean) of a group of numbers is defined as (sum of data) / (# of data points). With statement (2), we only have the numerator of this expression (the # of people in the group is unknown), so we can't figure out the average.
Looking at statement (1) alone, we can set up the average as follows:
Average = (sum of data points) / (# of data points)
= [(n/3)(74.5) + (2n/3)(70)] / (n) <-- note that I used inches here, so I won't have to write in more fractions than necessary (trying to write fractions on this forum is not fun)
= [(1/3)(74.5) + (2/3)(70)] / (n)
There's no need to simplify further, because the 'n' is gone: you get one number. Therefore, this statement is sufficient.
Answer = A
Note that, if you have the averages of all the FRACTIONS or PERCENTAGES of a group, then you'll be able to calculate the overall average of the group. This is a worthwhile fact to memorize for the data sufficiency problems.
Ron has been teaching various standardized tests for 20 years.
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Yves Saint-Laurent
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