Quentin is playing baseball and is batting. He swings and hits the ball sending it flying to the outfield. Which is greater- the force of the ball on the bat or the force of the bat on the ball ?

The force of the ball on the bat is same as the force of the bat on the ball.  

Explanation:

A bat hits the ball and the ball moves to the out filed.

According to the Newton's third law, for every action there is an equal and opposite reaction.

The action and the reaction forces acts on the two different bodies but the magnitude of the force is same.  

As the ball is hitted by the bat, the bat exerts the force on the ball and the same force is exerted on the bat by the ball according to the Newton's third law.

So, the force of the ball on the bat is same as the force of the bat on the ball but the direction of force is opposite.  

it would be kevlar ^^