Final answer:
When Claire cashes a check received from selling a US Treasury security to the Federal Reserve, both the monetary base and bank reserves will increase.
Step-by-step explanation:
When Claire sells a US Treasury security to the Federal Reserve on the secondary market, she receives a check as payment. Cashing the check at her bank results in an increase in both the monetary base and bank reserves. The monetary base increases because the cash received is considered part of the monetary base, which includes currency in circulation and reserves held by banks. Additionally, the bank reserves increase because the cash deposited by Claire increases the bank's reserves. Therefore, the correct answer is option 2) Both the monetary base and bank reserves will increase.