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by Cheese12 » Fri Oct 21, 2011 9:39 am
Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

A) 78
B) 77 1/5
C) 66 1/7
D) 55 1/7
E) 52


OA: A

Hi all,
Please provide me with a quick method to solve such kind of questions... thanks!
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by sl750 » Fri Oct 21, 2011 10:27 am
Let the smallest number be s
The largest number is 3s+20
s _ 55 _ 3s+20

We want to maximize the range, therefore 3s+20-s = max range

2(s+10) = Range is a multiple of 2

From the choices only A and E satisfy the L.H.S. Between the two choices, we pick the one with the maximum range. Hence A
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by GMATGuruNY » Fri Oct 21, 2011 10:44 am
I posted a solution here:

https://www.beatthegmat.com/set-median-t ... tml#330466
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by GMATGuruNY » Fri Oct 21, 2011 10:56 am
sl750 wrote:Let the smallest number be s
The largest number is 3s+20
s _ 55 _ 3s+20

We want to maximize the range, therefore 3s+20-s = max range

2(s+10) = Range is a multiple of 2

From the choices only A and E satisfy the L.H.S. Between the two choices, we pick the one with the maximum range. Hence A
This reasoning seems a bit risky.
If answer choices A and E were 80 and 78, the larger of the two answer choices would be incorrect.
Moreover, when the GMAT asks for the greatest possible value, the greatest answer choice typically is a TRAP.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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