Choice A rationale:

 The client has a normal coagulation profile.

This choice is incorrect because the client's prolonged PTT suggests a problem with the intrinsic pathway of coagulation, which is typical in hemophilia.

A normal coagulation profile would show normal values for both PTT and PT.

Choice B rationale:

 The client may have a vitamin K deficiency.

This choice is not applicable in this context.

A vitamin K deficiency primarily affects the extrinsic pathway of coagulation, leading to an elevated PT, but it does not typically affect the PTT, which is prolonged in hemophilia.

Choice C rationale:

 The client likely has hemophilia.

This is the correct choice.

Hemophilia is characterized by a deficiency or dysfunction of clotting factors, most commonly factor VIII (hemophilia A) or factor IX (hemophilia B)

Prolonged PTT with normal PT is a classic laboratory finding in hemophilia.

Choice D rationale:

 The client is at risk for thrombosis.

This choice is incorrect.

Hemophilia is associated with bleeding tendencies, not an increased risk of thrombosis.

Prolonged PTT indicates a reduced ability to form clots, making thrombosis less likely.