In a set of 10 consecutive odd positive integers, the product of the least and the greatest integers is 63? What is the

[Gmat_mission]

In a set of 10 consecutive odd positive integers, the product of the least and the greatest integers is 63? What is the arithmetic mean (average) of the set?

A. -12
B. 0
C. 8
D. 12
E. 30

Answer: D

Source: e-GMAT

[Scott@TargetTestPrep]

In a set of 10 consecutive odd positive integers, the product of the least and the greatest integers is 63? What is the arithmetic mean (average) of the set?

A. -12
B. 0
C. 8
D. 12
E. 30

Answer: D

Solution:

Since 63 = 1 x 63 = 3 x 21 = 7 x 9, we see that the only possible pair for the least and greatest integers are 3 and 21, respectively, and the set is {3, 5, 7, 9, 11, 13, 15, 17, 19, 21}. Since this is an evenly spaced set, the mean of the set is equal to the average of the least and greatest integers of the set. Therefore, the mean is (3 + 21)/2 = 12.

Answer: D