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At 12 noon, the alarm of a 12-hour clock is set for 3 p.m. Because of a defect, the alarm-setting hand…

On a 12-hour dial with 60 minute divisions, one minute division for the alarm hand represents \(12\text{ hours} / 60 = 12\text{ minutes}\) of alarm-setting time. Moving 1…

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At 12 noon, the alarm of a 12-hour clock is set for 3 p.m. Because of a defect, the alarm-setting hand keeps moving clockwise by one of the dial's 60 minute divisions every half-hour. The clock itself keeps correct time. At what time will the alarm ring?

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Correct answer D

On a 12-hour dial with 60 minute divisions, one minute division for the alarm hand represents 12 hours/60=12 minutes12\text{ hours} / 60 = 12\text{ minutes} of alarm-setting time. Moving 1 minute division every half-hour shifts the alarm setting forward by 24 minutes (0.4 hours0.4\text{ hours}) per real hour. If the alarm rings tt hours after 12 noon, t=3+0.4tt = 3 + 0.4t, giving 0.6t=30.6t = 3 or t=5 hourst = 5\text{ hours}, which is "5.00 pm".

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