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The average of 5 consecutive odd numbers is 27. What is the largest of these numbers?
29
31
33
35
31
For any odd count of consecutive numbers, the average is always the exact middle number. Thus, the third number is 27, and the numbers are 23, 25, 27, 29, 31.
Number of consecutive odd terms n = 5, Average = 27
Average=nSum┬аof┬аnumbersтАЛ
For any odd count of consecutive numbers, the average is always the exact middle number. Thus, the third number is 27, and the numbers are 23, 25, 27, 29, 31.
Students often assume the average is the first term or waste time setting up lengthy algebraic equations with x,x+2,x+4, etc.
Identify the Middle Term
For any odd number of consecutive terms, the average is always the middle term. Since the average is given as 27, the third number in the sequence is 27.
Middle┬аNumber=27
Determine the Sequence
Since they are consecutive odd numbers, the sequence increases by 2 for each subsequent term. Moving forward from the middle term, we get 29 and 31. Moving backward, we get 25 and 23.
23,25,27,29,31
Identify the Largest Number
The largest of these five consecutive odd numbers is the fifth term, which is 31.
31
B is correct because the largest of the 5 consecutive odd numbers with an average of 27 is calculated to be 31.
Recognizing properties of the middle term in arithmetic progressions saves valuable time in quantitative aptitude sections of competitive exams.
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