Average and the median

[4meonly]

Hello, GMAT takers!
I've found 1 intersting question and i have some problems with it. Here it is:
The average of 5 positive integers is 70. If the median is 84, what is the greatest possible value of the smallest number?
a. 42
b. 45
c. 48
d. 49
e. 54

How to solve it?
thanx in advance!

[sudhir3127]

I go with D.49.

Assume that out of 5 numbers 3 numbers are 84.
now we have only 2 numbers and er need to make 98 ( 350-3*84)

hence the greatest possible value of minimum number can be 98/2 = 49

please let me know if u have any doubts...

[pepeprepa]

Yep exactly the same.

You want the greatest value of the smallest integer so you have to take the smallest values of the 2 integers which are above 84 given that is the median. So you have to take 84 two times.

Now you have:
(X + Y + 84 + 84 + 84)/5=70
X+Y=98

48,50 gives you 48 as the smallest number
49,49 gives you 49 as the smallest number

So chose 49

[arorag]

thats correct 49.
It will be interesting if question says 5 different intergers

[pepeprepa]

It would be 47 in this case of different integers, you agree?

[4meonly]

guys, 49 is correct - D
thanx for help
statistics is my pain ((