ankur.agrawal wrote:Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ?
m
10m/7
10m/7 - 9/7
5m/7 + 3/7
5m
Make the situation concrete by plugging in a value for m.
Let m=5.
For the median to be 5, we need to choose 3 distinct integers that are smaller than 5 and 3 distinct integers that are larger than 5. Since we're trying to maximize the average, we want each integer to be as large as possible.
The largest allowed value is 2m = 2*5 = 10. So the 3 largest integers must be 8, 9, 10.
For the 3 distinct integers smaller than 5, the largest possible are 2, 3, 4.
So our 7 integers are 2, 3, 4, 5, 8, 9, 10.
Average = (2 + 3 + 4 + 5 + 8 + 9 + 10)/7 = 41/7. This is our target.
Now we plug m=5 into all the answers to which yields our target of 41/7.
Only answer choice C works:
10m/7 - 9/7 = (10*5)/7 - 9/7 = 50/7 - 9/7 = 41/7.
The correct answer is
C.
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].
Student Review #1
Student Review #2
Student Review #3
