A set consists of 5 distinct positive integers a, b, c, d, e

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Jun 22, 2019 7:13 pm

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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

OA E

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Sat Jun 22, 2019 7:13 pm

swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sun Jun 23, 2019 9:01 am

Given

$b$ is least integer and $d$ is the highest number and the sum of $a+c+e= 24$
mean of $b+24+\frac{d}{5} = 8.8$
$b+d=20$
since $d$ is the highest number it can be $19$ and $b$ is least can be $1$
so $19-1= 18$

Therefore, __C__

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