A golf ball moving forward with 1 unit of momentum strikes and bounces backward off a heavy bowling ball that is initially at rest and free to move. The bowling ball is set in motion with a momentum of_____.

A. Less than 1 unit.
B. More than 1 unit.
C. 1 unit.
D. Not enough information.

A) less than one unit.

The golf ball hits with momentum of 1. It then excerts a force on the ball equal to (mass of golf ball*1 - losses) and (Newton's 3rd) the bowling ball excerts the same amount of force on the golf ball.
However, this acceleration of the bowiling ball will be less than that of the golf ball due to (Newton's 2nd):
F=ma
A=F/m (Larger M = smaller a => smaller momentum)

It is not clear to me that the impact of the golf ball is perpendicular to the surface of the Bowling ball. If the impact is not perpendicular then the answer answer would be 'd', not enough info.

The statement does say that the golf ball bounces backward from the bowling ball, so if this means that the golf ball strikes the surface of the bowling ball perpendicularly then the answer would be b.

Momentum, Mass, and energy are all conserved. So in the initial state the momentum of the golf ball is +1, the momentum of the bowling ball is 0, and the momentum of the system is +1. When the golf ball impacts the bowling ball and decelerates to 0 velocity, it's momentum will be 0, and the momentum of the bowling ball will be +1, leaving the momentum of the system at +1. Because the Bowling ball is so massive compared to the golf ball it will then accelerate backward until its momentum aproaches -1. This will leave the bowling ball with a momentum of slightly less than +2, but the momentum of the entire system will still be +1 exactly.