Number Series, Clocks & Calendars MCQs With Answers
Reasoning sections often mix number patterns with everyday time puzzles. These number series, clock and calendar MCQs cover finding the next or missing term in series of squares, doubles and differences, the angle between clock hands at a given time, when the hands overlap, striking clocks, leap years, and finding the day of the week after a number of days or on the same date in the next year. They are handy for NTS, GAT, PPSC and FPSC analytical and IQ portions.
Take a scored quiz instead →What is the next number in the series: 2, 4, 8, 16, …?
• The series doubles the previous number (x * 2).
• 16 * 2 = 32.
Find the next number in the series: 3, 7, 13, 21, 31, ?
The differences are 4, 6, 8, 10, increasing by 2 each time, so the next difference is 12.
31 + 12 = 43.
Find the next number in the series: 2, 3, 5, 9, 17, ?
The differences are 1, 2, 4, 8, doubling each time, so the next difference is 16.
17 + 16 = 33. (Each term is also 2 × previous − 1.)
What is the next term in: 3, 6, 12, 24, …?
Multiply by 2.
What is the next number in the series: 5, 10, 20, 40, …?
Doubling pattern.
Next number: 1, 4, 9, 16, …?
Squares: 1^2, 2^2, 3^2, 4^2, 5^2=25.
What is the next number: 2, 6, 12, 20, …?
Differences: 4, 6, 8, 10 (+2).
What is the next number: 5, 11, 17, 23, …?
Common difference of 6.
If a clock strikes 3 times, how many intervals?
1-2, 2-3 = 2 intervals.
What is the next number: 1, 3, 6, 10, 15, …?
Pattern +2, +3, +4, +5, +6.
A clock strikes once at 1 o’clock, twice at 2 o’clock, and so on. How many times will it strike in 24 hours?
Sum = 1+2+...+12 = (12*13)/2 = 78. In 24 hours = 78 * 2 = 156.
What is the next term in: 2, 5, 10, 17, 26, …?
Diffs: 3, 5, 7, 9, 11. 26+11=37.
The number of days in a leap year is:
Fact.
Find the next number in the series: 2, 6, 12, 20, 30, ?
The terms are 1 × 2, 2 × 3, 3 × 4, 4 × 5, 5 × 6, so the next is 6 × 7.
6 × 7 = 42.
Which is a leap year?
Divisible by 4.
Find the next number in the series: 4, 9, 19, 39, ?
Each term is twice the previous term plus 1: 4 × 2 + 1 = 9, 9 × 2 + 1 = 19, 19 × 2 + 1 = 39.
39 × 2 + 1 = 79.
If a clock shows 3:00, what is the angle between the hands?
3 * 30 = 90°.
If 1st Jan 2025 is Wednesday, 1st Feb 2025 is?
Jan has 31 days. 31 mod 7 = 3. Wed+3=Sat.
What is the next number in the series: 2, 6, 12, 20, 30, …?
Diffs are 4, 6, 8, 10. Next diff 12. 30+12 = 42.
What is the angle between the clock hands at 4:00?
Each minute is 6°. Each hour is 30°. 4 * 30 = 120°.
If 1st Jan 2026 is Thursday, what day is 31st Jan 2026?
30 days later = 30 mod 7 = 2 days. Thursday + 2 = Saturday.
If today is Monday, what day will it be after 15 days?
15 days mod 7 = 1 day. Monday + 1 = Tuesday.
What is the angle between hands of a clock at 6:00?
At 6:00, angle is a straight line, 180°.
If 15th August 2025 is a Friday, what is the day on 15th August 2026?
2026 is not a leap year, +1 day. Friday + 1 = Saturday.
What is the angle between the hands of a clock at 3:15?
Angle = |30H - 5.5M| = |30*3 - 5.5*15| = |90 - 82.5| = 7.5°.
If 1st Jan 2026 is Thursday, what day is 1st Jan 2027?
2026 is not a leap year, so 1 odd day. Thursday + 1 = Friday.
At what angle are the hands of a clock inclined at 8:20?
Angle = |30*H - 5.5*M| = |30(8) - 5.5(20)| = |240 - 110| = 130°.
If 10th March 2003 was Monday, what day of the week was 10th March 2004?
2004 is a leap year. Between 10th March 2003 and 10th March 2004, February 29, 2004 is included, giving 2 odd days. Monday + 2 days = Wednesday.
At what time between 4 and 5 o’clock will the hands of a clock be together?
At 4 o'clock, hands are 20 minute spaces apart. Minute hand gains 55 minute spaces in 60 minutes. Time taken to gain 20 spaces = (60 / 55) * 20 = 240 / 11 = 21 9/11 minutes past 4.
If 15th August 2011 was Monday, what day of the week was 15th August 2012?
2012 is a leap year. The period includes February 29, 2012, so there are 2 odd days. Monday + 2 days = Wednesday.
What is the angle between the hour hand and minute hand of a clock at 3:30?
Angle = |30*H - 5.5*M| = |30(3) - 5.5(30)| = |90 - 165| = 75°.
If 1st January 2004 was Thursday, what day of the week was 1st January 2005?
2004 is a leap year (366 days), which has 2 odd days. Thursday + 2 days = Saturday.
Find the missing number in the sequence: 3, 7, 15, 31, 63, ?
Each term is 2 * previous term + 1: (63 * 2) + 1 = 126 + 1 = 127.
A clock striking 6 times takes 10 seconds. How long will it take to strike 12 times?
6 strikes have 5 intervals of time = 10s => Each interval = 2s. 12 strikes have 11 intervals = 11 * 2s = 22 seconds.
Find the next number in the series: 7, 10, 8, 11, 9, 12, ?
The series alternately adds 3 and subtracts 2: 7 (+3) 10 (−2) 8 (+3) 11 (−2) 9 (+3) 12 (−2) 10.
What is the next number in the series: 1, 8, 27, 64, 125, ?
The terms are cubes of natural numbers: 1³, 2³, 3³, 4³, 5³, so the next term is 6³ = 216.
Find the next term in the series: 2, 3, 5, 7, 11, 13, ?
These are consecutive prime numbers (numbers divisible only by 1 and themselves). The next prime after 13 is 17; 15 (3 × 5) and 16 (2 × 8) are not prime.
What is the next number in the series: 1, 1, 2, 3, 5, 8, 13, ?
This is the Fibonacci series, in which each term is the sum of the two terms before it: 8 + 13 = 21.
Find the next number in the series: 4, 9, 25, 49, 121, ?
The terms are squares of consecutive prime numbers: 2², 3², 5², 7², 11², so the next term is 13² = 169.
Find the wrong number in the series: 3, 8, 15, 24, 34, 48
The pattern is n² − 1: 2² − 1 = 3, 3² − 1 = 8, 4² − 1 = 15, 5² − 1 = 24, 6² − 1 = 35, 7² − 1 = 48. So 34 is wrong; it should be 35.
What is the next number in the series: 6, 11, 21, 36, 56, ?
The differences between terms are 5, 10, 15, 20, so the next difference is 25: 56 + 25 = 81.
Find the next term in the series: 1, 2, 6, 24, 120, ?
Each term is multiplied by 2, 3, 4, 5 … in turn: 1 × 2 = 2, 2 × 3 = 6, 6 × 4 = 24, 24 × 5 = 120, 120 × 6 = 720. These are factorials: 1!, 2!, 3!, 4!, 5!, 6!.
What is the angle between the hour hand and the minute hand of a clock at 2:20?
Use the formula θ = |30H − 5.5M| = |30 × 2 − 5.5 × 20| = |60 − 110| = 50°.
How many times do the hour hand and the minute hand of a clock coincide (overlap) in a day of 24 hours?
In 12 hours the hands coincide 11 times, not 12, because between 11 o'clock and 1 o'clock they meet only once, at 12:00. So in 24 hours they coincide 22 times, once every 65 5/11 minutes.
A clock gains 5 minutes every hour. If it is set correctly at 8:00 a.m., what time will it show when the correct time is 2:00 p.m. the same day?
From 8:00 a.m. to 2:00 p.m. is 6 hours. Gaining 5 minutes each hour, the clock gains 6 × 5 = 30 minutes, so it shows 2:30 p.m.
If the time on a clock is 3:40, what time will its mirror image show?
For a mirror image, subtract the given time from 11:60 (that is, 12:00): 11:60 − 3:40 = 8:20.
How many odd days are there in a leap year?
A leap year has 366 days = 52 weeks + 2 days. These 2 extra days are called 'odd days'.
The calendar of the year 2025 will be repeated in which year?
2025 is an ordinary year that began on a Wednesday. Adding odd days: 2025 (1) + 2026 (1) + 2027 (1) + 2028 (2, leap year) + 2029 (1) + 2030 (1) = 7 odd days, i.e. a remainder of 0. So 2031 also begins on a Wednesday, and since it is also an ordinary year, its calendar is identical to 2025's.
On which day of the week did 14 August 1947, the day Pakistan came into being, fall?
Using odd days: 1600 years give 0 odd days; the next 300 years give 1; the years 1901–1946 (11 leap + 35 ordinary) give 22 + 35 = 57, i.e. 1 odd day; and 1 January to 14 August 1947 has 226 days, i.e. 2 odd days. Total = 0 + 1 + 1 + 2 = 4, which means Thursday (0 = Sunday, 1 = Monday … 4 = Thursday).
Which of the following century years is NOT a leap year?
A century year is a leap year only if it is divisible by 400. 1600, 2000 and 2400 are divisible by 400, but 1900 is not (1900 ÷ 400 = 4.75), so 1900 was an ordinary year.