Problems on Calendars - Level 3 Questions
41) Which year will have
the same calendar as the calendar of 2022?
A) 2022 B) 2024 C) 2021 D)
2026
Answer: A
Explanation:
Two years will have the same calendar
if the number of odd days between the two years is zero.
An ordinary year has 1 odd day, and a
leap year has 2 odd days.
Years Odd day
2022 1
2023 1
2024 2
2025 1
2026 1
2027 1
2028 2
2029 1
2030 1
2031 1
2032 2
At the end of the year 2032, the sum of
the odd days is 14, i.e., zero. Therefore, the year 2033 will have the same calendar
as 2022.
42) Which year will have
the same calendar as that of 2017?
A) 2023 B) 2025 C) 2024 D)
2028
Answer :
Explanation:
Two years will have the same calendar
if the number of odd days in the given year and between the two years is zero, and
both years must either be leap years or ordinary years.
Year Odd days
2017 1
2018 1
2019 1
2020 2
2021 1
2022 1
The number of odd
days from 2017 to 2022 is 0.
So, the year 2023 will have the same
calendar as that of 2017.
43) Which year will have
the same calendar as that of 1927?
A) 1934 B) 1932 C) 1935 D) 1938
Answer: D
Explanation:
Two years will have the same calendar
if the number of odd days between the two years is zero.
An ordinary year has 1 odd day, and a
leap year has 2 odd days.
Years Odd day
1927 1
1928 2 (Leap Year)
1929 1
1930 1
1931 1
1932 2 (Leap Year)
1933 1
1934 1
1935 1
1936 2 (Leap Year)
1937 1
The number of odd days from 1927 to
1937 is 0.
So, the year 1938 will have the same
calendar as that of 1927.
44) Which of the
following years will have the same calendar as that of 2020?
A) 2025 B) 2034 C) 2032 D) 2048
Answer : D
Explanation:
2020 is a leap year.
To have the same calendar, both years
must be leap years.
The calendar of a leap year repeats
itself after 28 years because, in 28 years, we have 21 ordinary years and 7
leap years, which results in 0 odd days.
Hence, 2020 + 28 = 2048 will have the
same calendar as that of 2020.
Therefore, the correct answer is D)
2048.
45. The year 209N is a leap year. Which
of the following years will definitely be a leap year?
A)
209N + 4 B) 209N + 8 C)
209N + 12 D) 209N + 6
Answer: C
Explanation :
209N is a leap year. Then the possible values of N are 2 and
6.
Case 1:
If N=2, then the year 2092 is a leap year.
Taking option A : 2092 + 4 = 2096 is a leap year
Taking option B : 2092 + 8 = 2100 is not a leap year
Taking option C : 2092 + 12 = 2104 is a leap year
Case 2:
If N=6, then the year 2096 is a leap year.
Taking option A : 2096 + 4 = 2100 is a not leap year
Taking option B : 2096 + 8 = 2104 is not a leap year
Taking option C : 2096 + 12 = 2108 is a leap year
In both cases, the option
C is correct
So the answer is D
46) Which month will
share the same calendar as February in a leap year?
A) April B) August C) September D) None
Explanation:
For two months to have the same
calendar, the cumulative number of odd days from the given month to the
subsequent months should be zero.
Month Odd
days
February 1
March 3
April 2
May 3
June 2
July 3
At the end of July, the number of odd
days is 0.
Therefore, the subsequent month,
August, will have the same calendar as that of February.
47) On which day of the
week does 17th May 2018 fall?
A) Saturday B) Sunday C) Monday D)
Thursday
Answer : D
Explanation:
17th May 2018 = 2017 years + (1st
January 2018 to 17th May 2018)
2017 years = 2000 years + 17 years
2000 years = (5 x 400 years) = (5 x 0)
= 0 odd days. (400 consecutive years has 0 odd days)
17 years = 4 leap years + 13 ordinary
years. (A leap year has 2 odd days and an ordinary year has 1 odd day)
= (4 x 2) + (13 x 1) = 21 odd days i.e,
0 odd days
The number of odd days from 1st January
to 17th May 2018.
Month Odd Days : January 3 + February 0
+ March 3 + April 2 + May 3 = 11 i.e, 4 odd days
The total number of odd days = (0 + 0 +
4) = 4 i.e, 4 odd days
|
Odd
days left |
Day
of the week |
|
0 |
Sunday |
|
1 |
Monday |
|
2 |
Tuesday |
|
3 |
Wednesday |
|
4 |
Thursday |
|
5 |
Friday |
|
6 |
Saturday |
So the day of the week on 17th May 2018
is a Thursday
48) Find the day of the week on
15th August 1947.
a)
Monday b)
Tuesday
c) Thursday d)
Friday e) Sunday
Answer : D
Explanation:
The day of the week is counted according
to the number of odd days left
|
Odd
days left |
Day
of the week |
|
0 |
Sunday |
|
1 |
Monday |
|
2 |
Tuesday |
|
3 |
Wednesday |
|
4 |
Thursday |
|
5 |
Friday |
|
6 |
Saturday |
Given date:
15th August 1947
Years
Calculation:
1946
years =
1600 years + 300 years + 46 years
1600 years
have 0 odd days because they are multiples of 400 (400 years have 0 odd days).
300 years =
300 consecutive years consists of 1 odd day
46 years = 11
leap years + 35 non leap years = (11 x 2 )+ (35 x 1) = 57 i.e 1 odd days
Months
Calculation:
Counting the
days for each month from January to August: 31 + 28 + 31 + 30 + 31 + 30 + 31 +
15 = 227 days.
Odd days in
227 days = 3 odd days
Total Odd
Days:
Summing the
odd days from years and months: 0+1+1+3 = 5 odd days.
Determine the
Day:
5 odd days
mean, 15th August 1947 is Friday
49)
On which dates of May 2010 did Sundays fall?
a)
1, 8, 15, 22, 29
b)
2, 9, 16, 23, 30
c)
3, 10, 17, 24
d)
4, 11, 18, 25
e)
5, 12, 19, 26
Answer:
B
Explanation:
To determine
the day of the week on 1st May 2010:
1st May 2010
=> 2009 years, 4 months, and 1 day.
= 2000 years
+ 9 years + January + February + March +
April + May 1st
= 0 odd days
+ 2 leap years + 7 ordinary years + 31 days + 28 days + 31 days + 30 days + 1
day
= 0 + 4 odd
days + 7 odd days + 3 odd days + 0 odd days + 3 odd days + 2 odd days + 1 odd
day
= 20 odd days
= 6 odd days.
Th number of
days is 6, and the day of the week is Saturday.
Thus, the
first Sunday falls on 2nd April.
In that
month, Sunday falls on 2nd, 9th, 16th, 23rd, and 30th.
50) Find the day of the week on
17th March 1721.
A) Friday B) Thursday C) Saturday
D) Tuesday
Answer :
Explanation
:
17th March
1721 = 1720 years + 1st January 1921 to 17th March 1921.
1700 years =
(1600 + 100) years = (0 + 5) = 5
odd days.
(1600
consecutive years have 0 odd days and
100 consecutive years have 5 odd days )
20 years = 5
leap years + 15 ordinary years
=> (5 x
2) + (15 x 1) = 25 i.e, 4 odd days
The number
of days from 1st January, 1921 to 17th March 1921
January
31 days + February 28
days + March 17 days
=> 76 days i.e., 6 odd days.
So the total number of odd days= (5+4+6)= 15
i.e, 1 odd days
Hence,17th
March 1721 is Monday
51) There were 53 Sundays in a leap year. What day of the week was it
on April 16th of that year?
A) Monday B)
Friday C)
Sunday D) A or C
Explanation
:
In a leap
year, only days of the week of 1st and 2nd
January repeats 53 times.
So January 1st of the given year must be a
Saturday or Sunday.
If 1st
January was a Saturday :
Number of
days from 2nd January to 16th April =
(30 + 29 + 31+ 16) =106
The number of odd days is 1.
If 1st
January was a Saturday:
Then 16th
April would be => Saturday + 1 = Sunday
April 16th was
(Saturday + 1) = Sunday
If 1st January
was a Sunday :
Then 16th
April would be => Sunday + 1 = Monday
Therefore, the 9th
of April was Sunday or Monday.
52) Mr. Ravi is working as a Probationary Officer in a bank. Every Sunday
and 1st, 3rd, and 5th Saturdays are holidays, and all other days are working
days. Assuming Ravi does not take any leaves, then how many days does Mr. Ravi
work in August and September if the non-leap year begins on Friday?
A) 52 B)
48 C)
51 D) 44
Answer :D
Explanation:
The year is
a non-leap year and begins on Friday.
Number of
days from 2nd January to 1st August => (30 + 28 + 31 + 30 + 31 + 30 + 31 +
1) = 212
The number
of odd days in 212 days is 2.
1st
August will be =>
(Friday + 2) = Sunday.
Sundays in
August are => 1st, 8th, 15th, 22nd, and 29th
Saturdays in
August are => 7th, 14th, 21st, and 28th
Total
holidays in August = 5 Sundays + 2 Saturdays = 7
1st
September: Wednesday
Saturdays in
September :4th, 11th , 18th and 25th
Sundays in
September : 5th , 12th , 19th and 26th
1st and 3rd
Saturdays are holidays (Because we have no 5th Saturday)
4 Sundays
and 2 Saturdays are holidays.
So the
number of holidays in September is => 6
Total
working days in these 2 months = (Total days in August and September –
Holidays)
=> (31 +
30) – (7+6) = 48.
53) What is the probability of randomly selecting an ordinary year that
contains 53 Sundays?
A) 5/7 B)
4/7 C)
3/7 D) 1/7
Answer
:
Explanation:
An ordinary
year consists of 52 full weeks and 1 extra day.
Thus, each
day of the week (including Saturday) occurs 52 times in an ordinary year.
The
additional day can be any day of the week, depending on the year's starting
day.
Sample space
S: {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
Number of
elements in S = n(S) = 7
Therefore,
the probability of randomly selecting an ordinary year with 53 Sundays = 1/7.
54) What is the probability that a randomly chosen leap year includes 53
Wednesdays?
A) 1/7 B) 2/7 C) 3/4 D) 4/7
Answer
:
Explanation:
A leap year
consists of 52 complete weeks and two additional days.
The days of
the week on these two additional days depend on the first day of the year.
Sample space
S: {Saturday-Sunday, Sunday-Monday, Monday-Tuesday, Tuesday-Wednesday,
Wednesday-Thursday, Thursday-Friday, Friday-Saturday}
Number of
elements in S = n(S) = 7
Let A be the
set that includes Thursday as one day: {Tuesday-Wednesday, Wednesday-Thursday}
Number of
elements in set A = n(A) = 2
The
probability of randomly selecting a leap year with 53 Wednesdays = n(A)/n(S) =
2/7.
55) Mrs. Gupta was born on 29th February 1920, which happened to be a
Friday, and she lived for 78 years. How many birthdays did Mrs. Gupta celebrate
on Fridays in her lifetime?
A) 1 B)
2 C) 3 D) 4
Answer: B
Explanation:
Mrs. Gupta
was born in a leap year and 29th February.
So she
celebrated her birthday every four years only.
The same
calendar repeats itself after every 28 years (if the century year in this
period is not a leap year).
As she lived
for 78 years, she celebrated her last birthday on 29th February 1998.
So the same
calendar as that of 1920 occurred in the years:
1920 + 28 =
1948, 1948 + 28 = 1976
Mrs. Gupta
celebrated her birthday two times times on Fridays.
56) Two friends, Ramesh and Sneha, met on 22nd March 2022,
which was a Tuesday, and they decided to meet again in June but only on Monday.
On which of the following could they meet in June?
A) 6th, 13th, 20th, 27th
B) 7th, 14th, 21st, 28th
C) 8th, 15th, 22nd, 29th
D) 9th, 16th, 23rd, 30th
Explanation:
22nd March
2022 is Tuesday.
Number of days
from 23th March 2022 to 1st June 2022:
Month Number
of Days
March 31- 22 = 9
April 30
May 31
June 1
The total number of days is 71. So the number of odd days is 1.
So, 1st June
2022 will be on (Tuesday + 1) = Wednesday.
The first
Monday falls on 6th June.
Every 7th
day will be the same day countwise, so the 6th, 13th, 20th, and 27th are
Mondays.
57) In a particular year, January 1st is a Monday, but December 31st of
the same year is not a Monday. Then what is the day of the week on August 29th
of that year?
A) Tuesday B) Friday C) Wednesday D) Sunday
Answer: C
Explanation:
January 1st
and December 31st of that year are not on the same day of the week. So the year
is a leap year.
So the year
is a leap year.
January 1st
of the year falls on Monday.
The number
of days from the 2nd of January to August 22nd is:
Month Days
January 30
February 29
March 31
April 30
May 31
June 30
July 31
August 29
Total number
of days is 241.
Then the
number of odd days is 3.
Therefore,
the day of the week on August 29th is (Monday + 3) = Thursday.
58) Miss Radha celebrated her birthday on a Monday in February 2008. In
which year will she celebrate her birthday on a Tuesday at the earliest?
A) 2018 B) 2020 C) 2022 D) 2023
Answer :
Explanation:
Miss Radha
celebrated her birthday on a Monday in February 2008.
To celebrate
her birthday on a Tuesday, the number of odd days between the two dates must be
1.
From 2008 to
2009 -- 2 odd days (2016 is a leap year, and February 29th is considered)
2009 to
2010 1 odd day
2010 to 2011
1 odd day
2011 to 2012
1 odd day
2012 to 2013
2 odd days (2012 is a leap year and 29th February is considered)
2013 to 2014
1 odd day
From 2008 to
2014, the total number of odd days is 8, i.e., 1 odd day.
The year in
which Miss Radha will celebrate his birthday on a Tuesday at the earliest is
2014.
59) December 31st of a non-leap year is a Sunday. How many Mondays occur
in that year?
A) 51 times B) 52 times C) 53 times D) Can't be determined
Answer : B
Explanation:
1st January
and 31st December of a non-leap year falls on the same day of the week
So 1st January of the year is also Sunday
2nd January
is Monday
In a non-leap
year, the day of the week of 1st January repeats 53 times and all other days
repeat 52 times
So, Monday
occurs 52 times.
60) Meenakshi Dixit was born on 25th March 1995. Alia Chopra was born 150
days after Meenakshi Dixit. The Independence Day of that year was on Saturday.
On which day was Alia Chopra born?
A) Monday B) Saturday C) Wednesday D) Thursday
Answer : B
Explanation:
Meenakshi Dixit
was born on 25th March 1995.
Alia Chopra
was born 150 days after Meenakshi Dixit.
So Alia
Chopra was born on => 25th March 1995 + 120 days = 22nd August 1995.
The
Independence Day of that year was on Saturday => August 15th, 1995, was a
Saturday.
The number
of days from August 16th to 22nd August = 7 days.
The number
of odd days in 7 days = 0 odd days.
So Alia
Chopra was born on => (Saturday + 0) = Saturday.
