Practice Questions
Test your daily and yearly logic with these combination clock and calendar questions.
If the 1st of January 2007 was a Monday, what day of the week was the 1st of January 2008?
2007 is an ordinary year, which has 1 odd day. Monday + 1 Day = Tuesday.
Find the exact angle between the hands of a clock at 8:20.
Using $\theta = |30H - 5.5M|$: $|30(8) - 5.5(20)| = |240 - 110| = 130^\circ$.
Which of the following is not a leap year?
1900 is a century year. For it to be a leap year, it must be divisible by 400. 1900 is not divisible by 400.
How many times do the hands of a clock overlap in 24 hours?
In 12 hours, hands overlap 11 times. In 24 hours, they overlap 22 times.
A clock gains 4 minutes every hour. It was set correct at 8:00 AM. When the clock shows 2:00 PM, what is the correct time?
Clock gains 4 min/hr, so it runs at 64/60 of real speed. When clock shows 6 hrs passed, real time = $6 \times 60/64 = 5.625$ hrs = 5 hrs 37.5 min. Correct time = 8:00 AM + 5:37.5 = 1:37:30 PM.
At what time between 3 and 4 o'clock are the hands of the clock exactly opposite?
$180 = |30 \times 3 - 5.5M| \Rightarrow 180 = |90 - 5.5M|$. $90 - 5.5M = -180 \Rightarrow 5.5M = 270 \Rightarrow M = 270/5.5 \approx 49.09$ min past 3.
If 1 March 2023 was Wednesday, what day was 1 March 2024?
2024 is a leap year. From March 2023 to March 2024 = 366 days = 52 weeks + 2 odd days. Wednesday + 2 = Friday.
A watch loses 2 minutes every hour. It was set correct at 12 noon Monday. When it shows 6 PM Tuesday, what is the correct time?
Watch loses 2 min/hr, so runs at 58/60 of real speed. From Monday 12 noon to Tuesday 6 PM = 30 hrs shown. Real time = $30 \times 60/58 \approx 31.03$ hrs = 31 hrs 2 min. Correct time = 12 noon Monday + 31:02 ≈ 7:02 PM Tuesday.
The angle between hour and minute hand at 6:40 is?
$\theta = |30 \times 6 - 5.5 \times 40|^\circ = |180 - 220|^\circ = 40^\circ$.
If today is Friday, what day will it be after 3 months and 10 days (assuming no leap year)?
Assume months of 30 days each. 3 months = 90 days. Total = 100 days = 14 weeks + 2 odd days. Friday + 2 = Sunday.
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