Hey
strivingFor800The easiest way to find out the various combinations with sum = 90 is as follows:
Since \(90 = 2*3^2*5\), the various factors possible are 1,2,3,5,6,9,10,15,18,30,45,90
For the even number of consecutive integers, the mean/median is the average of the two
middle integers - which cannot be an integer.
For an odd number of consecutive integers, we will have a middle term that is an integer.
If N = 9, the middle term has a value of \(\frac{90}{9} = 10\)
The consecutive terms are from 6 to 14(9 in number with 10 as the middle term)
If N = 15, the middle term has a value of \(\frac{90}{15} = 6\)
The consecutive terms are from -1 to 13(15 in number with 6 as the middle term)
1. N could be 3 - 29,30,31(which adds up to give us 90)
N could be 9 - 6,7,8,9,10,11,12,13,14(again adds up to give us 90)
(Insufficient)2. 5 < N < 10. N could take values 6,7,8,or 9.
(Insufficient)Combining the information from both the statements and testing the other
values(N=6,7,8) we have a unique value of N.
(Sufficient - Option C) _________________
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