Sufficient vs Necessary

"A is sufficient to make B true" means as long as A, then B, regardless of any other contingency.
"A is necessary for B to be true" means for B to be true, then A. Other contingencies could still make B untrue, however.

A statement can be necessary AND sufficient, which make such statements of primary importance.

For example:
You're going to the fair. It costs 50 cents to get in.

It is SUFFICIENT to give the ticketmaster 50 cents to get in. I suppose we're ignoring cases where you're on America's Most Wanted and he recognizes you, thus preventing you from entering... so technically speaking, this is not a perfect example.

It is sufficient for a closed shape to be a triangle if it has three sides. It is also necessary.

Hmm... I want a perfect example of something that is just sufficient, however...