MGMAT PS

gmatmachoman wrote:Set S contains seven 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 ?


A ) m
B) 10m/7
C) 10m/7 – 9/7
D )5m/7 + 3/7
E )5m

variation : what if they are distinct integers??

Plz post both the answers

You just want to make the values in the set as large as possible, keeping in mind that the largest element cannot be larger than 2m, and that the middle element is m. The question really should make clear whether the integers need to be distinct (in mathematical set theory, sets do not contain repeated elements, though this is the type of technicality that is not tested on the GMAT; the GMAT would either say that 'S is a list of numbers' or 'S is a data set containing seven numbers', in which case it is clear that elements may be repeated, or it would spell out the fact that all of the elements are distinct).

So if we are allowed to have repeated elements, the largest values we can have are:

m, m, m, m, 2m, 2m, 2m

and if we are not allowed to repeat elements, the largest values we can have are:

m-3, m-2, m-1, m, 2m-2, 2m-1, 2m

Here we're assuming m is greater than 2 (you cannot construct a suitable set of seven distinct integers if m = 2).

Then to find the average, just sum the elements and divide by 7. In the first case you get 10m/7 and in the second you get 10m/7 - 9/7.

Where is the question from? The wording is unrealistic; if this were a real GMAT question, it would make clear whether repetition of elements is allowed. As it stands, it's hard to guess what the right answer should be; a mathematician would choose C, since he or she would assume this is a proper mathematical set, but in any similar real GMAT question I've seen, repetition of elements is always allowed unless the question tells you otherwise.