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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

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

by Gmat_mission » Sun Jan 24, 2021 2:43 pm

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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

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Source: Beat The GMAT — Problem Solving | Sun Jan 24, 2021 2:43 pm

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

by Scott@TargetTestPrep » Fri Feb 05, 2021 4:21 pm

Gmat_mission wrote: ↑
Sun Jan 24, 2021 2:43 pm
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

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