If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) 4x
(C) 5x/3
(D) 3x/2
(E) 3x/5
Let's let the 5 temperatures = J, K, L, M, and N, and let's say that J < K < L < M < N
If the mean of the 5 numbers is x, then (J+K+L+M+N)/5 = x
Multiply both sides of equation by 5, we get
J+K+L+M+N =
5x
We want to find a possible sum of the 3 greatest numbers (i.e., L+M+N)
L, M and N represent 3 of the 5 numbers. Since they are the
3 greatest values, we know that their sum must be greater than or equal to 3/5 of the sum of
J+K+L+M+N
So, L+M+N
> 3/5(
J+K+L+M+N)
Since
J+K+L+M+N =
5x we can say L+M+N
> 3/5(
5x)
In other words,
L+M+N > 3x
Also, since J+K+L+M+N = 5x, we can conclude that
L+M+N < 5x
This tells us that
3x < L+M+N < 5x
When we check the answer choices, only
B works.
Cheers,
Brent
