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Seven positive numbers a<=b<=c<=d<=e<=f<=g, has mean, median, mode all equal to 7. Then what is the largest possible value of g?

 Aug 6, 2020
 #1
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My guess:  1, 1, 2, 7, 7, 7, 24   --->   24

 Aug 6, 2020
 #2
avatar+1035 
+4

What I did (and kind of adding on to geno's answer):

We know that the median is 7. So, we can put 7 down as d.

We also see that for the mode to be 7, it has to occur the most. The most it can occur is 3, because if it occured less, than there would be 2 modes, and if it occured more, than g would not be that large. 

 

Now, for the mean to be 7, the a+b+c+7+7+7+g has to equal 49.

Subtract 21 from 49, and you get 28. From 28, you should see that to get the largest possible value of g, you need the smallest possible values of a, b, and c. Since the mode has to be 7, you can only have 2 1's. That leaves you over with one 2.

 

Subtract all of that from 28, and you get 24 for g.

 

:)

ilorty  Aug 6, 2020

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