Perform the operation: 3 gal, 1 qt. -1 gal, 3 qt. 5 gal 4 gal,4 qt. 1 gal. 2 qt. 1 gal

Ah, college mathematics.

We must remember there are four quarts per gallon.  Let's convert everything to gallons:

3 \frac 1 4 - 1 \frac 3 4 = \frac{13}{4} - \frac{7}{4} = \frac{6}{4} = 1 \frac 2 4

We don't reduce because it's easy to see that's 1 gallon, 2 quarts, third choice.