The average of four consecutive even numbers is 27. Find the largest of these sumber
Answers
This is a pretty easy one. First, if the average is 27, the two even numbers on each side that make that average are 26 and 28. However, you said 4 even numbers. Thus we need to add another pair of numbers to maintain that average. These are 24 and 30. Thus the largest consecutive even number making up that average is 30.
Bonus Round
Had you said 6 consecutive even numbers, the answer would have been 32. With 8 consecutive even numbers it would have been 34. With 10 consecutive even numbers it would have been 36. Is there a pattern here? Let's put it into a table to find out. We'll still use 27 as the average. However, the same rules would obviously apply for any given average. In the table below “a” is the average (in this case 27)
Consecutive Even----Max Even #----General Rule
—————2———————28————— a + 1
—————4———————30————— a + 3
—————6———————32————— a + 5
—————8———————34————— a + 7
—————10———————36————— a + 9
As can be seen from the table, the maximum even number (m) is equal to the average (a) plus amount of even numbers (n) minus 1.
m = a + n - 1
Hope that helps as a general rule for solving all puzzles of a similar nature