If the earth is pulling on Jimmy with a force of 600 N when he is standing on its surface, what will be the gravitational force pulling Jimmy on...

Newton's law of Universal Gravitation states that any two bodies, in the universe, will attract each other with a force given by:

where, F is the force of attraction, m1 and m2 are the masses of the bodies and r is the distance between them.

If the planet W has the same size as Earth, distance between Jimmy and center of planet W will the same as that on Earth. Planet W has a mass which is 1/4 that of Earth's mass. Since, the attractive force is directly proportional to the mass of bodies (and everything else is same between the two cases: Jimmy on Earth and Jimmy on W), the gravitational force puling Jimmy on planet W will be 1/4 or 25% of the gravitational force on Earth. 

i.e. gravitational force on Jimmy on W = 600/4 N = 150 N

Hope this helps.