Suppose that S is a finite set of positive integers. If the greatest integer in S is removed from S, then the average value (arithmetic mean) of the integers remaining is 32. If the least integer in S is also removed, then the average value of the integers remaining is 35. If the greatest integer is then returned to the set, the average value of the integers rises to 40. The greatest integer in the original set S is 72 greater than the least integer in S. What is the average value of all the integers in the set S? (А) 36.2 (В) 36.4 (C) 36.6 (D) 36.8 (E) 37
Suppose that S is a finite set of positive integers. If the greatest integer in S is removed from S, then the average value (arithmetic mean) of the integers remaining is 32. If the least integer in S is also removed, then the average value of the integers remaining is 35. If the greatest integer is then returned to the set, the average value of the integers rises to 40. The greatest integer in the original set S is 72 greater than the least integer in S. What is the average value of all the integers in the set S? (А) 36.2 (В) 36.4 (C) 36.6 (D) 36.8 (E) 37
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Suppose that S is a finite set of positive integers. If the greatest integer in S is removed from S, then the average value
(arithmetic mean) of the integers remaining is 32. If the least integer in S is also removed, then the average value of the integers
remaining is 35. If the greatest integer is then returned to the set, the average value of the integers rises to 40. The greatest
integer in the original set S is 72 greater than the least integer in S. What is the average value of all the integers in the set S?
(А) 36.2
(В) 36.4
(C) 36.6
(D) 36.8
(E) 37
Expert Solution
Step 1
Let the least integer in the set be y. Then the greatest integer in the set is y+72.
Let there are n integers in the set S and x be the sum of the integers.
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