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The average of four consecutive odd numbers is 36. What is the greatest of these numbers?
37
39
43
41
39
For consecutive numbers, the average is the middle value. Since there are 4 numbers, the average 36 falls between the 2nd and 3rd number. The sequence is 33, 35, 37, 39.
Four consecutive odd numbers, Average = 36
Average=nSumтАЛ
For consecutive numbers, the average is the middle value. Since there are 4 numbers, the average 36 falls between the 2nd and 3rd number. The sequence is 33, 35, 37, 39.
Many students mistake the average (36) as one of the odd numbers in the sequence. Since 36 is even, the numbers must be 33, 35, 37, 39, not 34, 36, 38, 40.
Define the numbers
Let the four consecutive odd numbers be x,x+2,x+4,x+6.
x,x+2,x+4,x+6
Form the equation
The average is given as 36. Thus, 4x+(x+2)+(x+4)+(x+6)тАЛ=36.
4x+12=144
Solve for x
Subtract 12 from both sides: 4x=132. Dividing by 4, we get x=33.
x=33
Identify the greatest number
The greatest number is x+6. Substituting x=33, we get 33+6=39.
33+6=39
B is correct because the sequence is 33, 35, 37, 39, and the greatest number is 39.
This logic is essential for 'Age Problems' and 'Missing Number' puzzles in reasoning where finding the central value simplifies the calculation significantly.
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