Is it 48?
Since the hands coincide every 65 5/11 minutes, they coincide 22 times in 24 hours after midnite. They are at right angles twice before each time they meet. Hence, the answer is 44.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993