Bunuel wrote:

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

(1) n is odd

(2) n >= 9

S = ( a(1)+a(n) )*n / 2 ==> 2a(1) + n - 1 = 90/n ==> a(1)= (90/n-n+1)/2

1)n is odd.

If n=5, then a(1)= (90/5-5+1)/2 = 7, check 7+8+9+10+11 = 45

If n=9, then a(1)= (90/9-9+1)/2 = 1, check 1+2+3+4+5+6+7+8+9 = 45 (NOT SUFF)

2)n >= 9

If n=9, then a(1)= (90/9-9+1)/2 = 1, check 1+2+3+4+5+6+7+8+9 = 45

If n=10, then a(1)= (90/10-10+1)/2 = 0, but a(1)>0 (SUFF)

For other n>9 a(1) will be <0, which contradicts our condition a(1)>0

Answer (B)

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