Data Sufficiency

IMO D

eitijan wrote:IMO D

Given: min (x,y) gives the minimum value
max (x,y) gives the maximum value

Max (a, b, c) = 8
Min (a, b, c) = 5
a > c

Required: max (a, b) + min (b, c)

Statement 1: min (a, b) = min (b, c) = 5
Case 1: a = b = 5 and b = 8
Case 2: b = c = 5 and a = 8
Case 3: b = 5, 5 < c < b and a = 8

But we know that a > c, hence Case 1 is not possible
From case 2 and 3 both, max (a, b) + min (b, c) = 8 + 5 = 13
Sufficient

Statement 2: min (c, b) = b and max (a, c) = 8
These tell us that b < c, and a = 8
Hence b = 5, the smallest of the values
Hence we have the following relation:
5 < c < 8
Therefore, max (a, b) + min (b, c) = 8 + 5 = 13
Sufficient

Correct Option: D