A clock is set going at 12 noon. Through how many degrees will its hour hand have turned by 2:30 a.m. the next morning?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 435°
The hour hand turns 30° in each hour and 0.5° in each minute. The time runs past midnight, so the hand goes once round the dial and then further.
From 12 noon to 12 midnight: 12 hours, one full round \(=12\times30^\circ=360^\circ\)
From 12 midnight to 2:00 a.m.: \(2\times30^\circ=60^\circ\)
From 2:00 a.m. to 2:30 a.m.: \(30\times0.5^\circ=15^\circ\)
Total turn \(=360^\circ+60^\circ+15^\circ=435^\circ\)
75° is only the turn after midnight; it leaves out the full round from noon to midnight
