How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?  Choose the correct choice from the following options.
A) 55  B) 56  C) 4  D) 5  E) 3
Solution:   At 11 O'clock, the hour hand is 5 spaces apart from the minute hand.   During the next 60 minutes, i.e. between 11' O clock and 12' O clock the hour hand will move five spaces [integral values as denoted by the 56 minute, 57 minute, 58 minute, 59 minute and 60 minute positions].   For each of these 5 positions, the minute hand will be at the 12th minute, 24th minute, 36th minute, 48th minute and 60th minute positions.   Hence the difference between the positions of the hour hand and the minute hand will have an integral number of minutes between them.   i.e. 5 positions.   Answer 5
<result>D</result>
How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?