Question

If the current is cut in half and the resistance is increased by a factor of three, how will the power be affected?

Answer 1

One formula for the power dissipated in an electric circuit is

         Power  =  (current)² x (resistance) .

I think that's the one we should use, because it has exactly
all of the quantities that we know or need to find.

OK.       
               Original power  =  (original current)² x (original resistance)
and
               New power  =  (new current)²  x  (new resistance)

                                 =  (0.5 x old current)² x (3 x old resistance)

                                 = (0.25) (old current)² x (3) (old resistance)

                                 =  (0.75) (original current)² (original resistance)

                                 =  (0.75) (original power) .

Summary:        New power  =  (0.75) (original power)

That looks just like
choice B: 
                 The power will decrease to 75 percent of its previous value.