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 ?
+128399 [2, 4, 6, .....54] has an average of 28
Removing 28 will also produce an average of 28
+14899 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?
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\((2+n-x)/2=28\\ n-x=54\\ x=n-54\)
\(x=n-54 \) | 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.
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