median quest

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engg.manik: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Thu Jul 02, 2009 10:38 pm; Location: Bangalore; Thanked: 1 times

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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Source: Beat The GMAT — Problem Solving | Sun Oct 04, 2009 9:56 am

mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

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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sanjana: Master | Next Rank: 500 Posts; Posts: 182; Joined: Sun Aug 02, 2009 7:19 pm; Thanked: 18 times; GMAT Score:680

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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rohan_vus: Master | Next Rank: 500 Posts; Posts: 189; Joined: Thu Apr 03, 2008 2:03 pm; Location: USA; Thanked: 21 times

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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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

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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