## A set consists of $$5$$ distinct positive integers $$a, b, c, d, e,$$ where $$b$$ is the least number and $$d$$ is the

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### A set consists of $$5$$ distinct positive integers $$a, b, c, d, e,$$ where $$b$$ is the least number and $$d$$ is the

by Gmat_mission » Wed Sep 23, 2020 5:50 am

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A set consists of $$5$$ distinct positive integers $$a, b, c, d, e,$$ where $$b$$ is the least number and $$d$$ is the highest number. If the sum of $$a, c$$ and $$e$$ is $$24,$$ and the mean of all $$5$$ numbers is $$8.8,$$ then what is the maximum value of $$d - b?$$

A. 16
B. 17
C. 18
D. 19
E. 20

Source: e-GMAT

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### Re: A set consists of $$5$$ distinct positive integers $$a, b, c, d, e,$$ where $$b$$ is the least number and $$d$$ is t

by Scott@TargetTestPrep » Mon Sep 28, 2020 11:46 am
Gmat_mission wrote:
Wed Sep 23, 2020 5:50 am
A set consists of $$5$$ distinct positive integers $$a, b, c, d, e,$$ where $$b$$ is the least number and $$d$$ is the highest number. If the sum of $$a, c$$ and $$e$$ is $$24,$$ and the mean of all $$5$$ numbers is $$8.8,$$ then what is the maximum value of $$d - b?$$

A. 16
B. 17
C. 18
D. 19
E. 20

Solution:

Since the sum of the 5 integers is 8.8 x 5 = 44 and the sum of a, c and e is 24, the sum of b and d is 44 - 24 = 20. Since we want the maximum value of d - b, we can let d = 19 and b = 1 and thus the maximum value of d - b = 19 - 1 = 18.