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fast way?

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by bacali » Sun Nov 30, 2008 11:45 am
This one took me about the full two minutes. Is there an easier way to go about these kinds of problems??


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


OA: B
Last edited by bacali on Sun Nov 30, 2008 11:56 am, edited 1 time in total.
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by cramya » Sun Nov 30, 2008 11:55 am
Not sure if this is the fastest

k+m+r+s+t / 5 = 16 and k<m<r<s<t (so r is the median)

k+m+r+s+t = 80

k+m+r+s+40=80

k+m+r+s = 40

We have to maximize r keeping the constraint r<s

k cant be 0 since it says positive integers
k=1 m=2

Remaining 40-3 = 37 can be split as 19 and 18

r can be at the max 18

I am getting B)

Whats your approach to [spoiler]C)[/spoiler]
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by bacali » Sun Nov 30, 2008 11:57 am
cramya wrote:Not sure if this is the fastest

k+m+r+s+t / 5 = 16 and k<m<r<s<t (so r is the median)

k+m+r+s+t = 80

k+m+r+s+40=80

k+m+r+s = 40

We have to maximize r keeping the constraint r<s

k cant be 0 since it says positive integers
k=1 m=2

Remaining 40-3 = 37 can be split as 19 and 18

r can be at the max 18

I am getting B)

Whats your approach to [spoiler]C)[/spoiler]
Yeah, sorry, I mixed it up while posting another Q. It's fixed.
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