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3 groups of 7 numbers each are made from positive integers from 1 to 2
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28 Nov 2019, 11:47
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55% (hard)
Question Stats:
50% (01:53) correct 50% (01:55) wrong based on 28 sessions
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3 groups of 7 numbers each are made from positive integers from 1 to 21, inclusive. What is the highest possible median of the medians of these 3 groups? A. 10 B. 11 C. 12 D. 14 E. 17.5
Re: 3 groups of 7 numbers each are made from positive integers from 1 to 2
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29 Nov 2019, 00:44
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lnm87 wrote:
3 groups of 7 numbers each are made from positive integers from 1 to 21, inclusive. What is the highest possible median of the medians of these 3 groups? A. 10 B. 11 C. 12 D. 14 E. 17.5
globaldesi There are 3 groups and a median of each of these 3 groups. Now let them be \(M_1<M_2<M_3\), so we are looking for the MAX possible value of \(M_2\).
What would surely be more than M_2?
a) The group containing \(M_2\) will have three numbers more and three numbers less than \(M_2\), so 3 numbers are greater than \(M_2\).
b) The group containing \(M_3\) will have three numbers greater than \(M_3\), and \(M_2<M_3\)so at least 4 numbers are greater than \(M_2\).
Total = 3+4=7, and hence the largest possible value of \(M_2\) is \(21-7=14\)
Re: 3 groups of 7 numbers each are made from positive integers from 1 to 2
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29 Nov 2019, 06:51
globaldesi wrote:
Can you please explain the solution for this question.
3 groups having 7 numbers each are to be made in such manner that we get largest possible median for G3 and least possible for G1. Since three medians are to be found, that constraint would lead to arranging numbers in ascending order(at least the colored part). Rest of the part of the groups would be interchangeable which does not affect our case anyhow.
For G1 4 ≤ median ≤ 10, any value would not matter. The colored part is what matters most giving us 14 as maximum median possible among the three medians.
Hope this helps...
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50% (01:53) correct 
