If the average (arithmetic mean) of 102 consecutive odd integers is 414, then the least of these integers is	Choose the correct choice from the following choices.
A) a) 160
B) b) 289
C) c) 250
D) d) 313
E) e) 525
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 51st and 52nd 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= 
<gadget id="calculator">50*2</gadget>
<output>100</output>
100 below this (every odd number is every other number). Therefore   413-100= 
<gadget id="calculator">  413-100</gadget>
<output>313</output>
313, answer choice d) 313
<result>D</result>
If the average (arithmetic mean) of 102 consecutive odd integers is 414, then the least of these integers is