MGMAT good sum, consecutive terms

[rb90]

The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

(2) n < 9

Correct answer is E.
Please explain the working.I also wanted to know we could use the n(n+1)/2 formula here

[hi.itz.mani]

Lets see

1st thing , can we use n(n+) / 2 ..... NO ....Reason n(n+ 1) / 2 is a special case of the sum of the consecutive numbers when the first number in sequence is 1.

Since it hasn't been stated in the question that the consecutive numbers need to start with 1. we can't use this formula.

Coming To the question:
Let a be the 1st number in the series and N be the number of integers in the sequence

so n/2( 2a + n - 1 ) = 45 or n ( 2a + n - 1 ) = 90

Statement 1. n is even
we know that n should be the factor of 90
hence n can be 2 , 6 , 10 , 18 , 30 and even 90
for n = 2 a => 22
for n = 6 a => 5
hence we can't determine the value of N with this .

Statement 2: N < 9
n = 1 a => 45
n = 2 a => 22
n = 3 a => 14
n = 5
n = 6

hence we can't determine the value of N with this .

If we join Statement 1 and statement 2 , we still can have n = 2 or n = 6

Hence the answer is E