Could you avoid cavities by chewing sugarfree gum and eating apples?

You can: Along with eating sugar free gum and apples, don't miss out on daily brushing and flossing.

Not alone: To prevent cavities you need to mechanically remove the soft film that grows on your teeth 24/7. This contains various bacteria.The gum and apples would be a help in preventing cavities, but you have to examine the rest of your diet. And these are not substitutes for brushing and flossing.

Xylitol gum: Sugarless will not prevent cavities but xylitol gum will. Xylitol is a natural sugar that has been shown in many studies to inhibit the growth of the decay causing bacteria and help your mouth maintain a more natural, healthier bacterial population. You need 6 grams of xylitol a day to get the beneficial effect. You can find xylitol products in health food stores, or the health food isle.

Somewhat: There is no substitute for brushing and flossing. If you are in a situation where that can't happen, then sugarless gum and apples can help clean teeth somewhat.