Problem Solving

BTGmoderatorDC wrote: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

The mean of all 5 numbers is 8.8
(a + b + c + d + e)/5 = 8.8
Multiply both sides by 5 to get: a + b + c + d + e = 44

The sum of a, c and e is 24
(a + c + e) = 24
So, take a + b + c + d + e = 44 and rewrite as: (a + c + e) + b + d = 44
We get: (24) + b + d = 44
So, b + d = 20

b is the least number and d is the highest number
Since b and d are POSITIVE INTEGERS, and since we're tying to MAXIMIZE the value of (d - b), we want to MAXIMIZE d and MINIMIZE b
This is accomplished when d = 19 and b = 1

What is the maximum value of (d - b)?
d - b = 19 - 1 = 18

Answer: C

Cheers,
Brent

BTGmoderatorDC wrote: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 C

Source: e-GMAT

We know that a + c + e = 24. Because the mean of the 5 numbers is 8.8, we see that their sum must be 5 x 8.8 = 44. Thus, a + b + c + d + e = 44.

Subtracting the first equation from the second equation, we obtain:
b + d = 44 - 24 = 20.

To maximize the difference of b and d, we will choose b to be as small as possible and d to be as large as possible. Thus, if b = 1 then d = 19, and the maximum value of (d - b) is 18.

Answer: C