mmslf75 wrote:If the mean of set S does not exceed mean of any subset of set S , which of the following must be true about set S ?

I. Set S contains only one element

II. All elements in set S are equal

III. The median of set S equals the mean of set S

Source : gmatcub

OA [spoiler]( 2nd and 3 rd statement)[/spoiler]

Fail to understand whynot 1st statement ??!

question is not COULD but MUST, more than one element may be their in set e.g. 2 2 2 2 2 and still the given condition hold.

Statement 2 shoudln't be correct.

Correct me if I am wrong - Set S - 1, 2, 3, 4, 5
Subset S - 3, 4, 5

Mean of set S - 3, mean of subset S - 4

mehravikas wrote:Statement 2 shoudln't be correct.

Correct me if I am wrong - Set S - 1, 2, 3, 4, 5
Subset S - 3, 4, 5

Mean of set S - 3, mean of subset S - 4

Hi Vikas

You have to consider all subset not a specific subset.And more over you are proving other way .It is given in the question that mean of the set does not exceed the mean of any subset.You have choose a set whose mean will not be more than mean of any subset.
As you have consider the set of 1,2,3,4,5.Mean of the set is 3. and subset 3,4,5 ;the mean of the subset is 4.This satisfy the question .But if you take a sub set of 1,2,3,the mean is 2.hence mean of the set is more than the subset.But you to satisfy the question that the mean of set is not more than the mean of any subset.Hence you have to change your set.

The criteria of question can only will be satisfied when all the elements of the set are equal.Even if you take a single different number the criteria will not be satisfied.
like take a set of 2,2,2,2,2,2,2,4.the mean of set is 18/8=2.25,If you take a subset 2 (only one number).the mean is 2.The mean of the set is more than mean of subset.Consider another set:2,2,2,2,2,2,2,1,mean of the set is 15/8=1.875,if you take one subset of 1(only one number);the mean is 1.Again not satisfying the criteria.

Hope it will help

tks
Ram

thanks mate

ramsharma wrote:

mehravikas wrote:Statement 2 shoudln't be correct.

Correct me if I am wrong - Set S - 1, 2, 3, 4, 5
Subset S - 3, 4, 5

Mean of set S - 3, mean of subset S - 4

Hi Vikas

You have to consider all subset not a specific subset.And more over you are proving other way .It is given in the question that mean of the set does not exceed the mean of any subset.You have choose a set whose mean will not be more than mean of any subset.
As you have consider the set of 1,2,3,4,5.Mean of the set is 3. and subset 3,4,5 ;the mean of the subset is 4.This satisfy the question .But if you take a sub set of 1,2,3,the mean is 2.hence mean of the set is more than the subset.But you to satisfy the question that the mean of set is not more than the mean of any subset.Hence you have to change your set.

The criteria of question can only will be satisfied when all the elements of the set are equal.Even if you take a single different number the criteria will not be satisfied.
like take a set of 2,2,2,2,2,2,2,4.the mean of set is 18/8=2.25,If you take a subset 2 (only one number).the mean is 2.The mean of the set is more than mean of subset.Consider another set:2,2,2,2,2,2,2,1,mean of the set is 15/8=1.875,if you take one subset of 1(only one number);the mean is 1.Again not satisfying the criteria.

Hope it will help

tks
Ram