There may be a better way to do this, but I simply evaluated the value of each answer.
Set up the question this way:
[T(1) + T(2) + T(3) + T(4) + T(5)]/5 = x
T(1) + T(2) + T(3) + T(4) + T(5) = 5x
If T(3), T(4), T(5) are the greatest values, they must be equal to or greater than T(1) or T(2).
A) 6x
T(1) + T(2) + 6x = 5x
So, T(1) + T(2) = -x
False. T(1) and/or T(2) must be negative to achieve this value. This negates the requirement that all temperatures are positive.
B) 4x
T(1) + T(2) + 4x = 5x
So, T(1) + T(2) = x
True. This could be a value, as the highest temps can be higher than the lowest temps and the lowest temps can be positive.
C) 5x/3
T(1) + T(2) + 5x/3 = 5x
So, T(1) + T(2) = 10x/3
False. The lowest two temps, combined, would be greater than the highest three temps, combined. This is impossible.
D) 3x/2
T(1) + T(2) + 3x/2 = 5x
So, T(1) + T(2) = 7x/2
False. The lowest two temps, combined, would be greater than the highest three temps, combined. This is impossible.
E) 3x/5
T(1) + T(2) + 3x/5 = 5x
So, T(1) + T(2) = 22x/5
False. The lowest two temps, combined, would be greater than the highest three temps, combined. This is impossible.
Answer: B.
