VIC + averages problem from GMAC paper exam

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

by tonebeeze » Tue May 10, 2011 3:44 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. 5x/3
d. 3x/2
e. 3x/5

OA = B

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Source: Beat The GMAT — Problem Solving | Tue May 10, 2011 3:44 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue May 10, 2011 5:09 pm

tonebeeze 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

First , since the mean of the 5 numbers is x, we know that (A+B+C+D+E)/5 = x
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.

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Tue May 10, 2011 5:45 pm

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?

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue May 10, 2011 6:16 pm

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?

Sure, we can say that if 0<A<B<C<D<E then C+D+E > (3/5)(A+B+C+D+E)
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

Brent Hanneson - Creator of GMATPrepNow.com

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Tue May 10, 2011 6:20 pm

Thanks Brent,
This rule is now in my memory bank. :)

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