If the average (arithmetic mean) of 102 consecutive odd integers is 414, then the least of these integers is  Choose the correct choice:
A) 160
B) 289
C) 250
D) 313
E) 525

Rationale: "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 102 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 51 st and 52 nd numbers in the set ) . this means that numbers 51 and 52 in this set are 413 and 415 . because we know that number 51 is 413 , we know that the smallest number is 50 odd numbers below this , which means that it is 50 * 2 = 100 below this ( every odd number is every other number ) . therefore 413 - 100 = 313 , answer choice d"
Answer: D