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

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

Answer: C

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Wed Sep 23, 2020 5:50 am

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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

Answer: C

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.

Answer: C

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