If the sum of a set of 7 consecutive odd integers is 105, what is the median integer of th… — GMAT

If the sum of a set of $7$ consecutive odd integers is $105$ , what is the median integer of the set?

Answer: 15

The median integer of the set is 15.

For any set of evenly spaced numbers, such as consecutive odd integers, the arithmetic mean is equal to the median. Since the sum of the

7

integers is

105

, the mean is

105 \div 7 = 15

. Therefore, the median of the set is

15

Apply the property of evenly spaced sets.

For consecutive odd integers, the mean of the set is equal to its median.

The numbers in an arithmetic sequence are symmetrically distributed around the middle value.

Calculate the arithmetic mean.

Mean =

\frac{\text{Sum}}{\text{Number of terms}} = \frac{105}{7} = 15

Dividing the sum of the terms by the count gives the average value.

Determine the median.

Median =

15

Because mean equals median for evenly spaced sets, the median must be 15.

Average and Median Equivalence in Evenly Spaced Sets

Estimated Time:45s

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