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 am; Followed by:2 members

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

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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