If the sum of five consecutive integers is 115, what is the value of the largest integer i… — GMAT

If the sum of five consecutive integers is $115$ , what is the value of the largest integer in this set?

The largest integer in the set is 25.

For any evenly spaced set with an odd number of elements, the arithmetic mean equals the median. Dividing the sum of

115

5

gives a median of

23

. The five consecutive integers are

21, 22, 23, 24, 25

, so the largest integer is

25

Find the average (and median) of the five consecutive integers.

Dividing the sum

115

5

yields a median of

23

For an odd number of consecutive integers, the average of the set is equal to its median (the middle term).

Determine the five consecutive integers centered around the median.

The integers are

21, 22, 23, 24, 25

Consecutive integers differ by

1

, so the two terms above the median

23

are

24

and

25

Identify the largest integer.

The largest integer is

25

The question asks specifically for the maximum value in the set.

Average and Median Equivalence in Consecutive Integer Sets

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