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S is a set of n consecutive positive integers. Is the mean

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by BTGmoderatorDC » Sun Jun 23, 2019 9:07 pm

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S is a set of n consecutive positive integers. Is the mean of the set a positive integer?

(1) the range of S is an even integer

(2) the median of S is a positive integer

OA D

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Source: — Data Sufficiency |

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by Ian Stewart » Thu Jun 27, 2019 7:21 am
A set of consecutive integers is equally spaced, so its mean and median are always equal. So Statement 2 is instantly sufficient.

The median will also be halfway between the smallest and largest values in the set, so if S is the smallest value, and R is the range, the median will be S + (R/2). If R is even, that's an integer, so Statement 1 is sufficient. Or you could notice that if we have an odd number of values in a set, the median is always in the set. If the range of a set of consecutive integers is even, then that set must contain an odd number of things, and the median must equal one of the integers in the set. So the answer is D.
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