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
OA = B
VIC + averages problem from GMAC paper exam
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First , since the mean of the 5 numbers is x, we know that (A+B+C+D+E)/5 = xtonebeeze 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. 5x/3
d. 3x/2
e. 3x/5
OA = B
If we take this equation and multiply top and bottom by 5, we get A+B+C+D+E = 5x
Second, let's say that the 5 temperatures are A, B, C, D, and E, and let's say that A<B<C<D<E
We want to know the possible sum of the 3 greatest numbers (i.e., C+D+E)
Since C, D and E are the 3 greatest values, we know that their sum must be greater than 1/2 of the sum of A+B+C+D+E (we can make even stronger conclusions than this, but that isn't necessary)
Since C+D+E is greater than the sum of 1/2(A+B+C+D+E), we know that C+D+E is greater than 1/2(5x) since A+B+C+D+E = 5x
In other words, C+D+E must be greater than 2.5x
This leaves us with answer choices A and B (the other options are less than 2.5x)
Now if A+B+C+D+E = 5x, and if A<B<C<D<E, then C+D+E must be less than 5x.
This leaves us with answer choice B
Last edited by Brent@GMATPrepNow on Thu Sep 19, 2013 6:58 am, edited 1 time in total.
- smackmartine
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Hi Brent,
When you say that :
Since C, D and E are the 3 greatest values, we know that their sum must be greater than 1/2 of the sum of A+B+C+D+E (we can make even stronger conclusions than this, but that isn't necessary)
I am just wondering, is there any rule as such?
When you say that :
Since C, D and E are the 3 greatest values, we know that their sum must be greater than 1/2 of the sum of A+B+C+D+E (we can make even stronger conclusions than this, but that isn't necessary)
I am just wondering, is there any rule as such?
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Sure, we can say that if 0<A<B<C<D<E then C+D+E > (3/5)(A+B+C+D+E)smackmartine wrote:Hi Brent,
When you say that :
Since C, D and E are the 3 greatest values, we know that their sum must be greater than 1/2 of the sum of A+B+C+D+E (we can make even stronger conclusions than this, but that isn't necessary)
I am just wondering, is there any rule as such?
Similarly, if 0<A<B<C<D<E<F<G then F+G > (2/7)(A+B+C+D+E+F+G)
Etc.
Cheers,
Brent
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