Final answer:
A patient who extends his arms and legs to a deep sternal rub, with no other response, would have a Glasgow Coma Scale score of 4 based on the responses in motor, verbal, and eye opening categories.
Step-by-step explanation:
When assessing a patient using the Glasgow Coma Scale (GCS), the score is based on three parameters: eye response, verbal response, and motor response. In your described scenario, if a patient only extends his arms and legs with no other response to a deep sternal rub, it suggests a motor response of abnormal extension posturing, which is scored as 2 on the GCS. There are no verbal responses (score of 1), and the eye response would also be a 1 if there is no eye opening. Therefore, the total GCS in this situation would be 2 (motor response) + 1 (verbal response) + 1 (eye response) = 4.