**Core Concept:**

The question is testing our understanding of coagulation cascade, clotting factors, and their abnormalities in pediatric patients. The coagulation cascade involves a series of reactions initiated by tissue factor and extrinsic pathway, leading to the formation of a stable fibrin clot to prevent excessive bleeding. The prothrombin time (PT) and activated partial thromboplastin time (APTT) are laboratory tests that evaluate the clotting function. PT reflects the intrinsic pathway, while APTT assesses the extrinsic and common pathways. Both tests are abnormal in cases of significant clotting factor deficiencies or inhibitor formation.

**Why the Correct Answer is Right:**

In this case, the child has elevated PT and APTT, which indicates a deficiency or dysfunction in clotting factors involved in both intrinsic and extrinsic pathways (PT) and common pathway (APTT). The most common cause of this presentation is a deficiency in factor VIII (Hemophilia A), as it affects both pathways. Factor VIII acts as an activator of factor IX, and its deficiency leads to a decrease in the intrinsic pathway (PT) and the common pathway (APTT).

**Why Each Wrong Option is Incorrect:**

A. Factor XI deficiency: This affects the intrinsic pathway, not the common pathway, resulting in elevated PT and normal APTT.
B. Factor XII deficiency: This affects the intrinsic pathway, not the common pathway, leading to elevated PT and normal APTT.
C. Factor IX deficiency: This affects the intrinsic pathway, not the common pathway, resulting in elevated PT and normal APTT.
D. Factor VII deficiency: This affects the intrinsic pathway, not the common pathway, leading to elevated PT and normal APTT.

**Clinical Pearl:**

In pediatric patients, a combination of elevated PT and APTT with normal bleeding time is highly suggestive of a deficiency in clotting factor VIII. Early diagnosis and management of hemophilia A can prevent complications and improve the quality of life in children with this condition.