Question

The average of 37 consecutive numbers is 54 . The larger number si :

• A. 61
• B. 72
• C. 83
• D. 97

Answer 1

Answer:

B. 72

Understanding Averages of Consecutive Numbers

• For a set of consecutive numbers (integers that follow each other in order, e.g., 1, 2, 3 or 10, 11, 12), the average is always equal to the middle number.

• This property holds true specifically when the count of consecutive numbers is an odd number.

• In this problem, we are given 37 consecutive numbers, which is an odd count.

• Therefore, the given average, 54, directly represents the middle number in this sequence.

Calculating the Largest Number

• Since there are 37 numbers in total and 54 is the exact middle number, we need to determine how many numbers are after 54 in the sequence.

• The number of terms before the middle term is equal to the number of terms after the middle term.

• The total numbers excluding the middle number are 37 - 1 = 36 numbers.

• These 36 numbers are split equally before and after the middle number: 36 / 2 = 18 numbers.

• So, there are 18 numbers smaller than 54 and 18 numbers larger than 54.

• To find the largest number, we add the count of numbers after the middle number to the middle number itself.

• Largest Number = Middle Number + (Number of terms - 1) / 2

• Largest Number = 54 + 18 = 72.