What's the angle between the hands of a clock at 3:15?

Say 7.5 degrees, not zero. The minute hand sits at 90 degrees, but the hour hand moves half a degree a minute, so after 15 minutes it's at 97.5. Check it with 30 times the hour minus 5.5 times the minutes.

The numbers, step by step

A full turn is 360 degrees. The minute hand moves 6 degrees a minute and the hour hand 30 degrees an hour.

Hour hand per minute30 degrees ÷ 60 minutes

0.5 degrees

Minute hand at 3:1515 × 6 degrees

90 degrees

Hour hand at 3:1590 + 15 × 0.5

97.5 degrees

Angle between them97.5 − 90

7.5 degrees

Check with the formula30 × 3 − 5.5 × 15

7.5 degrees

Same method at 9:4530 × 9 − 5.5 × 45

22.5 degrees

What the interviewer listens for

• Do you place the minute hand at 90 degrees?
• Do you notice the hour hand has moved past the 3?
• Do you use half a degree per minute?
• Do you land on 7.5 degrees and check it?

Common mistakes

• Answering zero because both hands seem to point at the 3.The hour hand has moved a quarter of the way to the 4.
• Moving the hour hand 30 degrees in 15 minutes.It moves 30 degrees an hour, so 7.5 degrees in 15 minutes.
• Going quiet while calculating.Saying each step out loud is a big part of what's being tested.

Likely follow-ups

• What's the angle at 12:30?The minute hand is at 180 degrees and the hour hand has moved 15 degrees past the 12, so the angle is 165 degrees.
• How many times do the hands overlap in 12 hours?11 times. The minute hand gains 5.5 degrees a minute, so it laps the hour hand about every 65.5 minutes, which fits 11 times in 12 hours.

More finance technicals

• A stock falls 50% and then rises 50%. Where does it end up?
• What's the difference between cash and accrual accounting?
• What creates a deferred tax asset?
• How do you account for a 30% stake in another company?
• Do unfunded pensions or leases belong in enterprise value?

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