median quest

[engg.manik]

22. Three positive integers: m, n, and q, their average is 10, median is m+6. What is the greatest possible value of Q?

[mehravikas]

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

[sanjana]

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.

[rohan_vus]

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

[mehravikas]

Otherwise this question cannot be solved...

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.