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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 860

In a class, Budi's score is greater than Doni's. The sum of Adi's and Doni's scores is greater than the sum of Budi's and Coki's scores. Meanwhile, Doni's score is greater than two times Budi's score substracted by Adi's score. Determine the median of those four students' scores.

All I know, was, by using their initials that:

B > D

A + D > B + C

D > 2B - A

And by using the second and third info I got that their score from lowest to highest is either C, D, B, A or D, B, C, A. However, I met a dead-end after that. Please someone help me.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,139

hi Monox D. I-Fly

As no numbers are given, there's no chance of a numeric answer to this. So I assume an answer is sought of the form (X+Y)/2 where X and Y are to be determined choosing from A, B, C and D.

(1) B > D

(2) A+D > B+C => A+D > B+C > D+C => A > C

(3) D > 2B - A => A+D > 2B > 2D => A > D

and

A > D > 2B - A => 2A > 2B => A > B

So we have A > B > D but it is unclear where C comes.

By experiment I have found a solution where C > D

{A=3, B=2, C=1.3, D=1.2}

but also a solution where D > C

{A=3, B=2, D = 1.2, C = 1.1}

so I am unable to determine whether the answer is (B+C)/2 or (B+D)/2

Sorry,

Bob

later edit: I'm a bit bothered by the sentence

Doni's score is greater than two times Budi's score subtracted by Adi's score

In English we wouldn't say "subtracted by" but rather "subtracted from" in which case the third inequality become (3) D > A - 2B. I'll have a play with this alternative.

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 860

Thank you everyone who has helped me with this question. I have asked this question in 4 different forums including this one and all confirm that it is impossible to find the exact number of the median's value.

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