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Nice Logic Based Question

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by theCodeToGMAT » Wed Sep 18, 2013 11:48 pm
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)35x
(D)23x
(E)53x
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by GMATGuruNY » Thu Sep 19, 2013 1:17 am
I believe that the answer choices should read as posted below:
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 the 5 temperatures be 1, 2, 3, 4, 5.
Since the values are consecutive, the average = the median.
Thus, x=3.
Here, the sum of the 3 greatest temperatures = 3+4+5 = 12.
The case above illustrates that the sum of the 3 greatest integers can be equal to answer choice B:
4x = 4*3 = 12.

The correct answer is B.
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by ganeshrkamath » Thu Sep 19, 2013 2:41 am
rahulmittal87 wrote: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)35x
(D)23x
(E)53x
average of 5 positive temperatures = x
sum of these = 5x

Let the first least two temperaturs be 0
sum of the highest 3 = 5x
But since the temperatures are all positive, the sum of the highest 3 temperatures < 5x
Only option that satisfies this is B

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by Brent@GMATPrepNow » Thu Sep 19, 2013 7:17 am
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.

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