Arithmetic average

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.

Thanks, man! Excellent explanation!

caspermonday wrote:Hi, this is a question from EST 31:

If arithmetic mean of five positive temperatures is x degrees Farenheit, then the sum of the three greatest of these temperatures could be:

a) 6x
b) 4x
c) 5x/3
d) 3x/2
e) 3x/5

OA b
Please explain. Thank you!

Here's another way we can reason it out:

The 5 numbers sum to 5x; therefore the answer must be smaller than 5x... eliminate (a).

The 3 biggest numbers in any set must sum to more than 3 times the average of the set (if all 5 numbers were equal, then the "biggest" 3 would sum to exactly 3*average). So, the answer must be greater than 3x... eliminate (c), (d) and (e).

Only (b) left - done!

Mmm.. this sounds much easier! Thank you!