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By how much does the average of the first 20 even numbers exceed the average of the first 20 odd numbers?

Competition practiceAverages & Ages
  • A1
  • B20
  • C2
  • D0

Step-by-Step Solution

The first 20 even numbers are 2, 4, ... , 40, evenly spaced, so their average is (2 + 40)/2 = 21. The first 20 odd numbers are 1, 3, ... , 39, and their average is (1 + 39)/2 = 20. The difference is 1. (In general the first n even numbers average n + 1 and the first n odd numbers average n.) 20 is the count of numbers in each list, and also the odd average on its own. 2 is the step between one number and the next within each list, but the two lists are offset by only 1, not 2 - each even number sits exactly 1 above the odd number beside it. 0 assumes the two averages must match, which would need the lists to overlap.
Answer: A) 1

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