Problem Solving

If 5 numbers are selected from 1, 2, 3, ...10, without replacement, what is the greatest possible value that the average of five numbers is greater than the median of five numbers?
(A) 1
(B) 3/2
(C) 2
(D) 5/3
(E) 3

Vavish,

I believe that the text is not correctly transcript.

Although, according to was is written the answer is C.

Lets see how.....

From 1,2,3,.....,10 you have to chose a serie of five that gives the greater possible mean but the least median and that can only be...

{1,2,3,9,10}, why? because it minimize the median (=3) and chosing the numbers 9 and 10 we can only maximize the mean (=5).

So 5-3=2

Hope it helps

no i still dont understand...can you explain...[/quote]

We know to find the median you have to reorder the numbers from least to greatest and pick the middle number - {1,2,3,9,10}

What about 9 and 10? because you're asked to find the mean (average) bigger than the median (in this case, bigger than 3).

Mean = 1+2+3+9+10/5 = 5.

If you find the difference between both average and median

5-3=2.

Thanks for help me with my reasoning, Carol.