kop wrote:The sum of the even numbers between 1 and k is 79*80, where k is an odd number, then k=?
(A) 79
(B) 80
(C) 81
(D) 157
(E) 159
Sum of evenly spaced integers = (number of integers)(average of biggest and smallest)
Prediction:
79 = the number of even integers and 80 = the average of the biggest and smallest.
Let x = the biggest integer.
Smallest integer = 2.
If the average of the biggest and smallest is 80, we get:
(x+2)/2 = 80.
x+2 = 160
x = 158.
Implication:
79*80 represents the sum of the even integers between 2 and 158, inclusive.
To confirm:
Number of even integers between 2 and 158, inclusive = 79.
Average of biggest and smallest = 80.
Sum = (number)(average) = 79*80.
Since k is the next biggest ODD integer, k=159.
The correct answer is
E.
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