A kinase is an enzyme that

ANS:B - uses ATP to add a phosphate group to the substrate

In fact kinases EXCHANGES (rather than adding) phosphate group from one high energy phosphate substrate to another low energy substrate.
It is true Kinases (hexokinase) "adds" (rather EXCHANGES) phosphate groups from one high-energy substrate (ATP) to low energy substrate (glucose).

In the case of pyruvate kinase, the same thing is true too. One substrate is ADP (low energy) and the other substrate is phospho-enol-pyruvate (high energy). Now the high energy molecule is phosphoenolpyruvate and the low energy molecule is ADP exchanges phosphate group. The phosphate exchange is carried out by a kinase.

Why do we say it adds instead of exchanges? That is what confuses everybody.

Let us see what phosphatase does?

I think phosphatase hydrolyses phosphate (Glucose-6-phosphate ) to Glucose and a FREE PHOSPHATE molecule. It DOES NOT exchange phosphate groups between substrates!

It is possible, those free phosphates combine with ADP to form ATP by the enzyme ATP synthase. I don't think phosphatase is capable of making ATP by itself. When we read glucogenesis, we assume that ATP is made by phosphatases from ADP. I suspect very much that is what really happening.

Disclaimer: This is just my speculation and open for debate! I need to read more to confirm that! You are welcome to criticise my explanation.

Thank you!