What we know:
If n consecutive integers have arithmetic mean of 10; those numbers are distributed either side of 10 perfectly symmetrically.
Range is the difference between the greatest and the least numbers in the series.
If the range is known the least of these integers must be less than the mean, i.e. 10 - (14/2) = 3 (Note we don't really need to calculate this... to know we can is sufficient.)
Similarly, the distance from the greatest number to mean equals to the distance from mean to the least number. So knowing the greatest number also sufficient to calculate the least number. (in this case 10 - (17 - 10) = 3)The answer is D
: Both Statement 1 and Statement 2 are sufficient ALONE .
The Official Guide For GMAT® Quantitative Review, 2ND Edition
If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?
(1) The range of the n integers is 14.
(2) The greatest of the n integers is 17.
Category: Arithmetic Statistics
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