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median quest

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median quest

by engg.manik » Sun Oct 04, 2009 9:56 am
22. Three positive integers: m, n, and q, their average is 10, median is m+6. What is the greatest possible value of Q?
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by mehravikas » Sun Oct 04, 2009 3:02 pm
Is the answer 22?

m + n + q = 30
also n = m + 6, therefore 2m + 6 + q = 30
2m + q = 24

For q to be the maximum, m has to be minimum. Assume m = 1, therefore q = 24 - 2 = 22
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by sanjana » Mon Oct 05, 2009 3:47 am
If not specified in the question can we consider the integers in the order m,n,q?

You have obviously assumed they are in that order as you have taken the median as n=m+6.
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by rohan_vus » Mon Oct 05, 2009 4:07 am
Obviously ! Its perfect to assume in this order . Among m , n and q based on given conditions , you know m cant be greatest as you have a median greater than m . So median could be q or n then . But since you are asked the greatest value of q , so q will be greatest only if its the biggest of the lot . Hence its logical to take q as the third one in this series to get the answer
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by mehravikas » Mon Oct 05, 2009 12:05 pm
Otherwise this question cannot be solved...
sanjana wrote:If not specified in the question can we consider the integers in the order m,n,q?

You have obviously assumed they are in that order as you have taken the median as n=m+6.
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