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The set {2, 4, 6, ..., n} contains the positive consecutive even integers from 2 through n.  When one of the integers from the set is removed, the average of the remaining integers in the set is 28. What is the least possible value of  n ?

 Nov 1, 2019
 #1
avatar+104932 
+2

[2, 4, 6, .....54]     has an average of 28

 

Removing 28  will also produce an average of 28

 

 

cool cool cool 

 Nov 1, 2019
 #2
avatar+8650 
+1

The set {2, 4, 6, ..., n} contains the positive consecutive even integers from 2 through n.  When one of the integers from the set is removed, the average of the remaining integers in the set is 28.

What is the least possible value of  n ?

 

Die Menge {2, 4, 6, ..., n} enthält die positiven fortlaufenden geraden ganzen Zahlen von 2 bis n. Wenn eine der Ganzzahlen, (x), aus der Menge entfernt wird, beträgt der Durchschnitt der verbleibenden Ganzzahlen in der Menge 28. Was ist der kleinstmögliche Wert von n?

 

Hello Guest!

 

\((2+n-x)/2=28\\ n-x=54\\ x=n-54\)

 

               \(x=n-54 \)   |   2     4     6      .   .   .   20

                   n = x + 54    |  56  58    60                74

\(\varnothing = (n+2-x)/2\)    |  28  28    28                28

 

The least possible value of  n is 56.

laugh  !

 Nov 1, 2019
edited by asinus  Nov 2, 2019

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