Clocks and calendars
Ten reasoning questions, each marked as you answer.
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What is the angle between the hour and minute hands of a clock at 7:40?
Answer and working
Answer B
Angle = |30H − 5.5M| = |210 − 220| = 10°. Answer: 10°. The hour hand moves too, half a degree a minute, which is why it is not 30°.
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1 January 2005 was a Saturday. What day of the week was 1 January 2006?
Answer and working
Answer D
2005 has 365 days: 1 odd day. Saturday + 1 = Sunday.
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What is the angle between the hour and minute hands of a clock at 6:45?
Answer and working
Answer B
Angle = |30H − 5.5M| = |180 − 247.5| = 67.5°. Answer: 67.5°. The hour hand moves too, half a degree a minute, which is why it is not 90°.
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What day of the week was 28 July 2003?
Answer and working
Answer A
1 January 2001 was a Monday. From then to 28 July 2003 is 938 days; 938 ÷ 7 leaves 0, so the day is 0 on from Monday: Monday.
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What is the angle between the hour and minute hands of a clock at 10:15?
Answer and working
Answer A
Angle = |30H − 5.5M| = |300 − 82.5| = 217.5°; the smaller angle is 360 − 217.5. Answer: 142.5°. The hour hand moves too, half a degree a minute, which is why it is not 150°.
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Today is Thursday. What day of the week will it be 66 days from today?
Answer and working
Answer B
66 ÷ 7 leaves 3. 3 days on from Thursday is Sunday.
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What is the angle between the hour and minute hands of a clock at 10:50?
Answer and working
Answer B
Angle = |30H − 5.5M| = |300 − 275| = 25°. Answer: 25°. The hour hand moves too, half a degree a minute, which is why it is not 0°.
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What day of the week was 12 November 2007?
Answer and working
Answer B
1 January 2001 was a Monday. From then to 12 November 2007 is 2,506 days; 2,506 ÷ 7 leaves 0, so the day is 0 on from Monday: Monday.
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What is the angle between the hour and minute hands of a clock at 7:30?
Answer and working
Answer D
Angle = |30H − 5.5M| = |210 − 165| = 45°. Answer: 45°. The hour hand moves too, half a degree a minute, which is why it is not 30°.
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1 January 2019 was a Tuesday. What day of the week was 1 January 2020?
Answer and working
Answer B
2019 has 365 days: 1 odd day. Tuesday + 1 = Wednesday.
More reasoning: Number and letter series, Coding and decoding, Analogies, Odd one out, Blood relations, Direction sense.