Quantitative Aptitude

Clocks and Calendars

428 Questions
All Angle between hands 150 Clock gaining or losing time 132 Clock hands coincidence 69 Right angle times 30 Find time from angle 21 Decoding mixed date formats 7 Find day using reference date 6 Repeating same calendar 6 Date without reference day 3

Clocks and Calendars Questions

Multiple choice

The reflex angle between the hands of a clock at 10:2: 5 is?

  1. 180°

  2. 1921.2°

  3. 195°

  4. 1971 2°

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At 10:25, the hour hand is at 10 + 25/60 = 10.4166 hours. Angle = |30H - 5.5M| = |30*10 - 5.5*25| = |300 - 137.5| = 162.5 degrees. The reflex angle is 360 - 162.5 = 197.5 degrees.

Multiple choice

Three clocks were set to true time. First runs with the exact time. Second slows one minute/day. Third gains one minute/day. After how many days will they show true time again?

  1. 360

  2. 180

  3. 720

  4. 480

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The second clock loses 1 minute per day, and the third gains 1 minute per day. For a clock to show the true time again, it must lose or gain exactly 12 hours (720 minutes). Since the clocks change by 1 minute per day, it takes 720 days for them to accumulate a 720-minute difference.

Multiple choice

At what time, between 3 o'clock and 4 o'clock, both the hour hand and minute hand coincide each other?

  1. 3:16 7/11

  2. 3:16 11/4

  3. 3:30

  4. 3:16 4/11

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At 3 o'clock, the hands are 15 minutes apart. The minute hand gains 5.5 degrees per minute on the hour hand. To coincide, the minute hand must cover the 15-minute gap. Time = 15 / (11/60) = 900/11 = 81 9/11 minutes past 12, but we need the time past 3. The formula is (60/11) * H. At 3, it is (60/11) * 3 = 180/11 = 16 4/11 minutes past 3.

Multiple choice

At what time between 2 and 3 o'clock will the hands of a clock be together?

  1. (9 + 10/11) min past 2

  2. (10 + 10/11) min past 2

  3. (11 + 10/11) min past 2

  4. (12 + 10/11) min past 2

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The hands of a clock are together when the minute hand has gained 10 minutes over the hour hand. The formula for the time past H o'clock is (60/11) * H. For H=2, this is 120/11 = 10 + 10/11 minutes past 2.

Multiple choice

A watch gains 12 seconds every 3 hours, what time will it show at 10 A.M. on Tuesday if the watch is set right at 3 A.M. on Sunday?

  1. 09 hrs 58 minutes

  2. 09 hrs 57 minutes 8 seconds

  3. 10 hrs 2 minutes

  4. 10 hrs 3 minutes 40 seconds

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From Sunday 3 AM to Tuesday 10 AM is 48 + 7 = 55 hours. The watch gains 12 seconds every 3 hours, so in 55 hours it gains (55/3) * 12 = 220 seconds = 3 minutes and 40 seconds. The watch will show 10:03:40 AM.

Multiple choice

At what time between 5 and 6 o' clock are the hands of a 3 minutes apart?

  1. 24 min

  2. 12 min

  3. 13 min

  4. 14 min

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The minute hand moves 6 degrees per minute, and the hour hand moves 0.5 degrees per minute. Relative speed = 5.5 degrees per minute. At 5 o'clock, the minute hand is at 0 and the hour hand is at 150 degrees. To be 3 minutes apart (18 degrees), the minute hand must be at 150 - 18 = 132 degrees or 150 + 18 = 168 degrees. Time = 132 / 5.5 = 24 minutes.

Multiple choice

A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 15 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?

  1. 5:00

  2. 5:34

  3. 5:42

  4. 6:00

  5. 6:24
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Kim's wristwatch always shows the correct time, including the 'am' and the 'pm'. Jim's watch is identical to Kim's watch in all aspects except its pace, which is slower than the pace of Kim's watch. At 12 noon on January 1st, Jim sets his watch to the correct time, but an hour later, it shows 12:57 pm. At 12 noon on June 1st, Jim resets his watch to the correct time. On how many instances between the two dates mentioned, including 12 noon, do Jim's and Kim's watches show the exact same time including the 'am' and the 'pm'?

  1. 10

  2. 7

  3. 15

  4. 9

  5. 17
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Directions: Select the correct alternative from the given choices. lf a leap year is chosen at random, what is the probability that there are exactly 52 Sundays in it?

  1. 1/7

  2. 2/7

  3. 5/7

  4. 6/7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A leap year has 366 days, which is 52 weeks and 2 extra days. The possible pairs for the 2 extra days are (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun). For there to be exactly 52 Sundays, the extra days must not include Sunday. There are 5 such pairs out of 7, so the probability is 5/7.