Averages

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

Hi RiyaR,

This question has a couple of great "concept" shortcuts built into it.

We're told that the average of 5 positive numbers is X, which means that the SUM of the 5 numbers is 5X.

The question asks us for a POSSIBLE sum of the greatest 3 values….

Since the values are all POSITIVE and they sum to 5X, there's no way for the sum of the greatest 3 to be bigger than that. 6X is NOT possible. Eliminate A.

IF all the values were the same (just call them all X), then the biggest 3 would sum to 3X. Changing the values would only INCREASE the sum of the biggest 3. This helps to eliminate C, D and E - they're all too small.

There's only one answer left…

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Hi vivekvijayan,

The wording in this question requires you to be a bit flexible with your thinking. It asks for what COULD be the sum of the three largest values, NOT "what is" the sum of the three largest values.

In your example, none of the given answers matches YOUR sum. This doesn't mean that you're wrong, it just means that your work did not match the answer that COULD be the sum of the three greatest.

GMAT assassins aren't born, they're made,
Rich