Determining exact clock overlap times using relative angular speed

Statement 1: The hour and minute hands coincide when the angle between them is 0^\circ. Using the formula θ = 30H - 5.5M = 0: 30(3) = 5.5M \implies 90 = 5.5M \implies M = 90/5.5 = 180/11 = 16.36 minutes. Since 16.36 minutes falls exactly between the 16th and 17th minute marks, Statement 1 is correct.

Statement 2: The minute hand and the second hand. The second hand completes a full 360^\circ sweep of the entire clock face during every single 1-minute interval. Consequently, it is physically guaranteed to pass over the slow-moving minute hand exactly once during any given minute (excluding perfect overlaps at the exact 60s boundary). Between 4:58 and 4:59, the minute hand sits near the 58-minute mark. As the second hand sweeps through its 60-second cycle, it will inevitably overtake the minute hand around the 58th second. Statement 2 is geometrically irrefutable.

Answer: (c).