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talaangoshtari
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talaangoshtari wrote:A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7/17. What was the number erased?
A. 7
B. 8
C. 9
D. 10
E. 11
After one value is removed:
Since all of the values are INTEGERS, the sum here must be an integer.
Sum = (number)(average).
Since the average = 35 7/17, and the sum must be an integer, the number of integers must be a MULTIPLE OF 17.
For any evenly spaced set, average = median.
After one of the consecutive integers is removed, most of the remaining set will still be evenly spaced.
As a result, the average of the remaining set -- 35 7/17 -- will still be close to the median.
Implication:
The number of integers = 4*17 = 68, with the result that 35 7/17 will be close to the median of the 68 mostly consecutive integers.
Thus:
Sum = (number)(average) = (68)(35 7/17) = 2408.
Original set:
Since 68 integers remain after one of the integers is removed, the original set contains 69 integers.
Sum of the first n positive integers = (n)(n+1)/2.
Thus:
Sum = (69)(70)/2 = 2415.
Removed integer = (original sum) - (sum after one integer is removed) = 2415-2408 = 7.
The correct answer is A.
