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D is corrent because tests of controls are directed toward the effectiveness of the design or operation of controls. In this case the control procedure is to determine that only authorized persons sign checks.
A is incorrect because a cash count is a test of transactions and balances which is a substantive test rather than a test of a control.
B is incorrect because sending confirmation letters to banks helps substantiate the existence of cash at year end. Therefore, this is a substantive rather than a test of a control.
C is incorrect because testing the clerical accuracy of inventory listings as of the balance sheet date is primarily a substantive test to determine whether inventory listings are accurately compiled.