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Clock — Questions and Answers

Clock questions in the quantitative section test two things: the angle between the hands at a given time, and how much a faulty clock gains or loses. Both reduce to constants — the minute hand sweeps 6° per minute and the hour hand 0.5°, so the minute hand gains 5.5° every minute. Nothing else needs memorising.

20 solved questionsArithmetic AptitudeFree · no signup

Clock— Concepts, Formulas & Shortcuts

  • Minute hand moves 6° per minute; hour hand moves 0.5° per minute (30° per hour).
  • Relative gain of the minute hand over the hour hand = 5.5° per minute.
  • Angle at H hours M minutes = |30H − 5.5M|; if the result exceeds 180°, subtract from 360°.
  • The hands coincide 11 times in 12 hours, are opposite 11 times, and form a right angle 22 times.
  • A correct clock's hands coincide every 65 5/11 minutes.
  • For a gaining or losing clock, scale the error in proportion to the time elapsed.

Clock Practice Questions with Answers

Attempt each question first, then open the explanation. All 20 questions below are free to read and require no signup.

  1. Q1.The angle between the hour and minute hands at 5:30 is:

    Moderate
    • A0°
    • B15°
    • C30°
    • D45°
    +Show Answer & Explanation

    Answer: B. 15°

    Explanation: |30 × 5 − 5.5 × 30| = |150 − 165| = 15°.

    Clock question 1 of 20

  2. Q2.At what time between 4 and 5 o'clock are the hands of a clock at right angles for the first time?

    Difficult
    • A4:05 5/11
    • B4:10
    • C4:38 2/11
    • D4:15
    +Show Answer & Explanation

    Answer: A. 4:05 5/11

    Explanation: |120 − 5.5M| = 90 → 5.5M = 30 → M = 60/11 = 5 5/11 minutes past 4.

    Clock question 2 of 20

  3. Q3.A clock gains 5 minutes every 24 hours. How much will it gain in 6 days?

    Easy
    • A20 minutes
    • B25 minutes
    • C30 minutes
    • D35 minutes
    +Show Answer & Explanation

    Answer: C. 30 minutes

    Explanation: 5 × 6 = 30 minutes.

    Clock question 3 of 20

  4. Q4.How many times in 12 hours are the hands of a clock in a straight line (coinciding or opposite)?

    Moderate
    • A11
    • B22
    • C24
    • D44
    +Show Answer & Explanation

    Answer: B. 22

    Explanation: They coincide 11 times and are opposite 11 times, giving 22 straight-line positions in 12 hours.

    Clock question 4 of 20

  5. Q5.The angle between the hands of a clock at 6:00 is:

    Easy
    • A90°
    • B120°
    • C150°
    • D180°
    +Show Answer & Explanation

    Answer: D. 180°

    Explanation: |30 × 6 − 0| = 180°, so the hands point in exactly opposite directions.

    Clock question 5 of 20

  6. Q6.A watch loses 3 minutes every 24 hours. If it is set right at 12 noon on Monday, what will it show at 12 noon on Wednesday?

    Moderate
    • A11:54
    • B11:57
    • C12:03
    • D12:06
    +Show Answer & Explanation

    Answer: A. 11:54

    Explanation: Two days elapse, so it loses 6 minutes and shows 11:54.

    Clock question 6 of 20

  7. Q7.The angle between the hands of a clock at 3:15 is:

    Moderate
    • A0°
    • B7.5°
    • C15°
    • D30°
    +Show Answer & Explanation

    Answer: B. 7.5°

    Explanation: |30 × 3 − 5.5 × 15| = |90 − 82.5| = 7.5°.

    Clock question 7 of 20

  8. Q8.How many degrees does the minute hand move in one minute?

    Easy
    • A0.5°
    • B1°
    • C6°
    • D30°
    +Show Answer & Explanation

    Answer: C. 6°

    Explanation: The minute hand covers 360° in 60 minutes, so 6° per minute.

    Clock question 8 of 20

  9. Q9.How many degrees does the hour hand move in one hour?

    Easy
    • A0.5°
    • B6°
    • C15°
    • D30°
    +Show Answer & Explanation

    Answer: D. 30°

    Explanation: The hour hand covers 360° in 12 hours, so 30° per hour.

    Clock question 9 of 20

  10. Q10.The angle between the hands of a clock at 9:00 is:

    Easy
    • A60°
    • B90°
    • C120°
    • D180°
    +Show Answer & Explanation

    Answer: B. 90°

    Explanation: |30 × 9 − 0| = 270°, and the smaller angle is 360 − 270 = 90°.

    Clock question 10 of 20

  11. Q11.A clock loses 10 minutes every 24 hours. How much will it lose in 3 days?

    Easy
    • A20 minutes
    • B25 minutes
    • C30 minutes
    • D40 minutes
    +Show Answer & Explanation

    Answer: C. 30 minutes

    Explanation: 10 × 3 = 30 minutes.

    Clock question 11 of 20

  12. Q12.How many times in 24 hours do the hands of a clock coincide?

    Moderate
    • A11
    • B22
    • C24
    • D44
    +Show Answer & Explanation

    Answer: B. 22

    Explanation: They coincide 11 times in each 12-hour cycle, giving 22 times in a day.

    Clock question 12 of 20

  13. Q13.At what time between 2 and 3 o'clock do the hands of a clock coincide?

    Difficult
    • A2:10 10/11
    • B2:12
    • C2:15
    • D2:16 4/11
    +Show Answer & Explanation

    Answer: A. 2:10 10/11

    Explanation: The minute hand must gain 60° at 5.5° per minute: 60/5.5 = 120/11 = 10 10/11 minutes past 2.

    Clock question 13 of 20

  14. Q14.The reflex angle between the hands of a clock at 10:25 is:

    Difficult
    • A180°
    • B192.5°
    • C197.5°
    • D202.5°
    +Show Answer & Explanation

    Answer: C. 197.5°

    Explanation: |30 × 10 − 5.5 × 25| = |300 − 137.5| = 162.5°, which is the smaller angle. The reflex angle is 360 − 162.5 = 197.5°.

    Clock question 14 of 20

  15. Q15.The angle between the hands of a clock at 2:00 is:

    Easy
    • A30°
    • B45°
    • C60°
    • D90°
    +Show Answer & Explanation

    Answer: C. 60°

    Explanation: |30 × 2 − 0| = 60°.

    Clock question 15 of 20

  16. Q16.The angle between the hands of a clock at 8:00 is:

    Easy
    • A90°
    • B100°
    • C110°
    • D120°
    +Show Answer & Explanation

    Answer: D. 120°

    Explanation: |30 × 8| = 240°, and the smaller angle is 360 − 240 = 120°.

    Clock question 16 of 20

  17. Q17.By how many degrees does the minute hand gain on the hour hand each minute?

    Moderate
    • A0.5°
    • B5°
    • C5.5°
    • D6°
    +Show Answer & Explanation

    Answer: C. 5.5°

    Explanation: The minute hand moves 6° and the hour hand 0.5° per minute, so the gain is 5.5°.

    Clock question 17 of 20

  18. Q18.A clock gains 2 minutes per day. How much will it gain in a week?

    Easy
    • A10 minutes
    • B12 minutes
    • C14 minutes
    • D16 minutes
    +Show Answer & Explanation

    Answer: C. 14 minutes

    Explanation: 2 × 7 = 14 minutes.

    Clock question 18 of 20

  19. Q19.The angle between the hands of a clock at 12:30 is:

    Difficult
    • A165°
    • B170°
    • C175°
    • D180°
    +Show Answer & Explanation

    Answer: A. 165°

    Explanation: |30 × 12 − 5.5 × 30| = |360 − 165| = 195°, and the smaller angle is 360 − 195 = 165°.

    Clock question 19 of 20

  20. Q20.How many times in 12 hours are the hands of a clock exactly opposite each other?

    Moderate
    • A10
    • B11
    • C12
    • D22
    +Show Answer & Explanation

    Answer: B. 11

    Explanation: The hands are opposite 11 times in every 12-hour cycle.

    Clock question 20 of 20

Clock — Frequently Asked Questions

What is the angle formula for clock hands?+

Angle = |30H − 5.5M| where H is the hour and M the minutes past it. At 5:30 this gives |150 − 165| = 15°.

How do I solve gaining and losing clock questions?+

Work out the error per 24 hours, then scale it linearly. A clock losing 3 minutes a day will be 6 minutes slow after 2 days, so at noon it will show 11:54.

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