Quantity A: 15/16 + 1/256
Quantity B: 1 - 1/64

I want to add 1/64 to both quantities (you'll see why shortly). So, let's first rewrite 15/16 as 60/64 to get:
Quantity A: 60/64 + 1/256
Quantity B: 1 - 1/64

Add 1/64 to both quantities to get:
Quantity A: 61/64 + 1/256
Quantity B: 1

Let's apply some number sense
If we were to add 1/64 to 61/64, we'd get 62/64, which is less than 1.
Since 1/256 is LESS THAN 1/64, we can conclude that 61/64 + 1/256 = some number that's less than 1

So, we have:
Quantity A: some number that's less than 1
Quantity B: 1

Answer: B