# How many positive integers between 100 and 999 inclusive are odd?

I found the answer to this in a pdf online but don't understand their method: Every 2nd number is odd. 1000 div 2 − 100 div 2 = 500 − 50 = 450

The method I thought I could use didn't work either. If someone can explain to me why my logic doesn't make sense I would appreciate it. I simply created an inequality as such:

100 ≤ 2k+1 ≥ 999

and then solved for k

99 ≤ 2k ≥ 998

49.5 ≤ k ≥ 449.5

since its integers only:

50 ≤ k ≥ 449

and then the numbers in this range would be (449-50)+1=400

• When you divide $998/2$ you should get $499$, not $449$ – Ross Millikan Mar 29 '16 at 3:12
• @RossMillikan d'oh! – ohbrobig Mar 29 '16 at 3:24

$$100 \leq 2k+1 \leq 999$$ $$99 \leq 2k \leq 998$$ $$\frac{99}{2} \leq k \leq 499$$
$\frac{900}{2} = 450$