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The average (arithmetic mean) of the 5 positive integers k,

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by harsh.champ » Thu Feb 04, 2010 2:38 pm
imane81 wrote:thanks for your help on this one...

The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m
< r < s < t. If t is 40, what is the greatest possible value of the median of the 5 integers?
A. 16
B. 18
C. 19
D. 20
E. 22

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k+m+r+s+t=16*5(80)
Now,t=40
=>k+m+r+s=40
Now,we know that the median of the 5 integers is r.
Since s>r
Therfore,minimum value of s will be r+1.
Hence,k+m+r+(r+1)=40
Also,since all the integers are positive,minimum value of k=1,m=2.
So,for maximum value of r, 1+2+r+(r+1)=40
=>2r+4=40
=>r=36/2=18

Hence,(B) should be the answer choice.
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by ajith » Thu Feb 04, 2010 3:18 pm
imane81 wrote:thanks for your help on this one...

The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m
< r < s < t. If t is 40, what is the greatest possible value of the median of the 5 integers?
A. 16
B. 18
C. 19
D. 20
E. 22
(k+m+r+s+40)/5 =16

k+m+r+s = 40

the median is the value of r

it is maximum when k,m are minimum and r,s are maximum

k=1; m=2; r =r , s=r+1
3+2r+1 =40
r=18

The maximum median =18
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by neelimareddym » Thu Feb 04, 2010 10:14 pm
imane81 wrote:thanks for your help on this one...

The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m
< r < s < t. If t is 40, what is the greatest possible value of the median of the 5 integers?
A. 16
B. 18
C. 19
D. 20
E. 22
IMO B

k+m+r+s+t = (16*5) = 80

So, k+m+r+s = 40

We are looking for the greatest possible value of r
So k=1,m=2 r+s = 37
r+s/2 =37/2 = 18.5
So r =18, s=19 will solve the case
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