Consider the following statements : 1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide. 2. Between 4:58 p.m. and 4:59 p.m.. both minute hand and second hand coincide. Which of the above statements is/are correct?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Statement 1 is correct. At 3:16 PM, the hour hand covers 192×0.5=96 192×0.5=96 degrees, and the minute hand covers 16×6= 96 16×6=96 degrees in the same time span. Therefore, both hands coincide at this time. Statement 2 is also correct. The second-hand travels through the entire clock face in one minute, so it will coincide with the minute hand between 4:58 PM and 4:59 PM. Therefore, both statements 1 and 2 are correct.
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