http://www.amazon.com/TRACK-FIXED-FI...o+single+speed

Well, I bought the above bike because of the positive reviews and its price. Yes, I know its not the best in the market but its cheap and I just want to start riding. What worries me is that my bike will sustain some sort of damage if I ride in the rain as dirt/grit/dust gets splashed into the chains etc. Would these types of fenders (Amazon.com : SKS X-Tra Dry Rear Bicycle Fender for 26 inch wheels : Bike Fenders : Sports & Outdoors) do a good enough job of keeping me and my bike dry, clean, and damage free given the fact that full sized fenders may not be installed?