PlacementPrepWhat is the angle between the hour and minute hands of a clock at 8:30?
Solution
Angle = |30H − 5.5M| = |30 × 8 − 5.5 × 30| = 75°.
Answer: (C) 75°
Logical Reasoning · Time
Clocks: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
At what time between 3 and 4 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 3:00 the gap is 90°.
Time = 90/5.5 = 16 4/11 minutes past 3.
Answer: (A) 16 4/11 minutes past 3
How many times are the hands of a clock at right angles in a day?
Solution
The hands are at right angles twice every hour, which would give 24 times in 12 hours.
But between 2 and 4 o'clock they are at right angles only 3 times, not 4 (3:00 is shared by both hours); the same happens between 8 and 10 o'clock (9:00). So there are 22 times in 12 hours.
In a day: 44.
Answer: (B) 44
A clock shows 10:15. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60 (or 23:60).
11:60 − 10:15 = 1:45.
Answer: (C) 1:45
A watch gains 6 minutes every 24 hours. It is set right at 6 a.m. on Monday. How many minutes ahead will it be after 72 hours?
Solution
It gains 6 minutes in 24 hours, so in 72 hours it gains 6 × 72/24 = 18 minutes.
Answer: (A) 18 minutes
What is the angle between the hour and minute hands of a clock at 6:25?
Solution
Angle = |30H − 5.5M| = |30 × 6 − 5.5 × 25| = 42.5°.
Answer: (C) 42.5°
At what time between 4 and 5 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 4:00 the gap is 120°.
Time = 120/5.5 = 21 9/11 minutes past 4.
Answer: (B) 21 9/11 minutes past 4
A clock shows 4:15. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60 (or 23:60).
11:60 − 4:15 = 7:45.
Answer: (B) 7:45
A watch gains 3 minutes every 24 hours. It is set right at 7 a.m. on Monday. How many minutes ahead will it be after 60 hours?
Solution
It gains 3 minutes in 24 hours, so in 60 hours it gains 3 × 60/24 = 7 1/2 minutes.
Answer: (C) 7 1/2 minutes
What is the angle between the hour and minute hands of a clock at 5:15?
Solution
Angle = |30H − 5.5M| = |30 × 5 − 5.5 × 15| = 67.5°.
Answer: (B) 67.5°
At what time between 1 and 2 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 1:00 the gap is 30°.
Time = 30/5.5 = 5 5/11 minutes past 1.
Answer: (C) 5 5/11 minutes past 1
A clock shows 9:40. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60 (or 23:60).
11:60 − 9:40 = 2:20.
Answer: (C) 2:20
A watch gains 5 minutes every 24 hours. It is set right at 9 a.m. on Monday. How many minutes ahead will it be after 18 hours?
Solution
It gains 5 minutes in 24 hours, so in 18 hours it gains 5 × 18/24 = 3 3/4 minutes.
Answer: (D) 3 3/4 minutes
What is the angle between the hour and minute hands of a clock at 6:40?
Solution
Angle = |30H − 5.5M| = |30 × 6 − 5.5 × 40| = 40°.
Answer: (A) 40°
A clock shows 9:15. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60 (or 23:60).
11:60 − 9:15 = 2:45.
Answer: (A) 2:45
A watch gains 6 minutes every 24 hours. It is set right at 7 a.m. on Monday. How many minutes ahead will it be after 60 hours?
Solution
It gains 6 minutes in 24 hours, so in 60 hours it gains 6 × 60/24 = 15 minutes.
Answer: (A) 15 minutes
What is the angle between the hour and minute hands of a clock at 6:50?
Solution
Angle = |30H − 5.5M| = |30 × 6 − 5.5 × 50| = 95°.
Answer: (A) 95°
At what time between 5 and 6 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 5:00 the gap is 150°.
Time = 150/5.5 = 27 3/11 minutes past 5.
Answer: (C) 27 3/11 minutes past 5
A clock shows 8:05. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60 (or 23:60).
11:60 − 8:05 = 3:55.
Answer: (D) 3:55
What is the angle between the hour and minute hands of a clock at 7:55?
Solution
Angle = |30H − 5.5M| = |30 × 7 − 5.5 × 55| = 92.5°.
Answer: (A) 92.5°
At what time between 6 and 7 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 6:00 the gap is 180°.
Time = 180/5.5 = 32 8/11 minutes past 6.
Answer: (A) 32 8/11 minutes past 6
A clock shows 10:20. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60 (or 23:60).
11:60 − 10:20 = 1:40.
Answer: (D) 1:40
What is the angle between the hour and minute hands of a clock at 6:45?
Solution
Angle = |30H − 5.5M| = |30 × 6 − 5.5 × 45| = 67.5°.
Answer: (C) 67.5°
How many times are the hands of a clock at right angles in 12 hours?
Solution
The hands are at right angles twice every hour, which would give 24 times in 12 hours.
But between 2 and 4 o'clock they are at right angles only 3 times, not 4 (3:00 is shared by both hours); the same happens between 8 and 10 o'clock (9:00). So there are 22 times in 12 hours.
In 12 hours: 22.
Answer: (D) 22
A clock shows 6:40. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60 (or 23:60).
11:60 − 6:40 = 5:20.
Answer: (B) 5:20
A watch gains 6 minutes every 24 hours. It is set right at 9 a.m. on Monday. How many minutes ahead will it be after 30 hours?
Solution
It gains 6 minutes in 24 hours, so in 30 hours it gains 6 × 30/24 = 7 1/2 minutes.
Answer: (B) 7 1/2 minutes
At what time between 9 and 10 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 9:00 the gap is 270°.
Time = 270/5.5 = 49 1/11 minutes past 9.
Answer: (A) 49 1/11 minutes past 9
A watch gains 3 minutes every 24 hours. It is set right at 6 a.m. on Monday. How many minutes ahead will it be after 36 hours?
Solution
It gains 3 minutes in 24 hours, so in 36 hours it gains 3 × 36/24 = 4 1/2 minutes.
Answer: (B) 4 1/2 minutes
At what time between 2 and 3 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 2:00 the gap is 60°.
Time = 60/5.5 = 10 10/11 minutes past 2.
Answer: (D) 10 10/11 minutes past 2
A watch gains 2 minutes every 24 hours. It is set right at 7 a.m. on Monday. How many minutes ahead will it be after 30 hours?
Solution
It gains 2 minutes in 24 hours, so in 30 hours it gains 2 × 30/24 = 2 1/2 minutes.
Answer: (A) 2 1/2 minutes
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