SOLUTION: Which of the following numbers is odd for every integer n? A) 2003n B) n^2 + 2003 C) n^3 D) n + 2004 E) 2n^2 + 2003

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Which of the following numbers is odd for every integer n? A) 2003n B) n^2 + 2003 C) n^3 D) n + 2004 E) 2n^2 + 2003       Log On


   

Question 302064: Which of the following numbers is odd for every integer n?
A) 2003n B) n^2 + 2003 C) n^3 D) n + 2004 E) 2n^2 + 2003
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Try an odd and even and a negative odd and a negative even in each.
If any is even move on.
A)2003 *1=2003
2003*2=4006
4006 is not odd so move on
B)2003 is always odd
Can n^2 ever be odd?
yes 3^2=9
which leaves 9+2003 even move on
C) n^3 if n=2 then we have 2^3=8 move on
D) n+2004 2004+2=2006 move on
So we are left with E
E)2003 is always odd
Can 2*n^2 ever be odd?
No! why ? because multiplying by 2 makes it even whether it was even or odd to begin with.