If the average (arithmetic mean) of 8 consecutive odd integers is 414, then the least of these integers is	Choose the correct choice from the following answers
A) 407 B) 518 C) 519 D) 521 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 8 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 4 th and 5 th numbers in the set ) . this means that numbers 4 and 5 in this set are 413 and 415 . because we know that number 4 is 413 , we know that the smallest number is 3 odd numbers below this , which means that it is 3 * 2 = 6 below this ( every odd number is every other number ) . therefore 413 - 6 = 407 , answer choice a
Answer: A