Calendar Questions and Answers

Answer: C

The year being crossed here contains a 29 February, so the shift is two days rather than one.

From 8 February 2004 to 8 February 2005 the span includes 29 February 2004, making it 366 days:

\[ 366 \equiv 2 \pmod 7 \]

Stepping back from the given Tuesday:

\[ \text{Tuesday} - 2 = \textbf{Sunday} \]

Subtracting only one day, the reflex from ordinary years, gives Monday - the trap this question is built around.

Answer: C

Correct answer: Friday

Count the odd days up to that date. 1600 years give 0, the next 300 give 1, and the 46 years from 1901 to 1946 give \(35 + 22 = 57\), that is 1 odd day.

From 1 January to 15 August 1947 is 227 days, and \(227 = 32 \times 7 + 3\), giving 3 more.

\[0 + 1 + 1 + 3 = 5 \text{ odd days}\]

Counting 0 as Sunday, 5 odd days lands on Friday.

Answer: A

Correct answer: Thursday

2008 is a leap year, so it contains 366 days.

\[366 = 52 \times 7 + 2\]

That leaves 2 odd days, so the day advances by two: Tuesday becomes Thursday. An ordinary year would advance the day by only one.

Answer: D

Count the odd days backwards from 2013 until they total a multiple of seven.

\[ 2012:2,\ 2011:1,\ 2010:1,\ 2009:1,\ 2008:2,\ 2007:1,\ 2006:1,\ 2005:1,\ 2004:2,\ 2003:1,\ 2002:1 \]

\[ \text{total} = 14 \quad\Longrightarrow\quad 0 \text{ odd days} \]

So 2013 repeats the calendar of 2002.

Answer: A

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)

Odd days in 1600 years = 0

Odd days in 300 years = (5 x 3) 1

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.

Jan. Feb. March April May June

(31 + 28 + 31 + 30 + 31 + 17) = 168 days

168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3.

Given day is Wednesday

Answer: B

18 Feb, 2016 = (2015 years + Period from 1.1.2016 to 18.2.2016)

Odd days in 1600 years = 0

Odd days in 400 years = 0

15 years = (12 ordinary years + 3 leap year) = (12 x 1 + 3 x 2)= 4 odd days

Jan  Feb

(31 + 18 ) = 49 days

49 days = (7 weeks + 0 day)= 0 odd day.

Total number of odd days = (0 + 0 + 4 + 0) = 4 odd day.

Given day is Thursday

Answer: A

19th April, 1986 = (1985 years + Period from 1.1.1986 to 19.4.1986)

Odd days in 1600 years = 0

Odd days in 300 years = 1

85 years has 21 leap years + 64 ordinary years.

Number of odd days in 85 years =( 21 x 2 + 64) = 1 odd day.

Jan. Feb. March April

(31 + 28 + 31 + 19) = 109 days

109 days = 15 weeks + 4 days= 4 odd day.

Total number of odd days = (1 + 0 + 1 + 4) = 6.

Given day is Saturday.

Answer: C

A year is a leap year if it is divisible by 4, except that a century year must also be divisible by 400.

\[ 1996 \div 4 = 499 \ \checkmark, \qquad 1984 \div 4 = 496 \ \checkmark, \qquad 2004 \div 4 = 501 \ \checkmark \]

\[ 1863 \div 4 = 465.75 \ \times \]

So 1863 is not a leap year. None of these is a century year, so the 400-rule never comes into play.

Answer: A

A year is a leap year if it is divisible by 4, except that a century year must also be divisible by 400.

\[ 1984 \div 4 = 496 \ \checkmark \text{ and not a century year} \]

1863 is not divisible by 4; 1900 and 2500 are century years not divisible by 400.

So only 1984 has 366 days.

Answer: C

25 Jan, 1981 = (1980 years + Period from 1.1.1981 to 25.1.1981)

Odd days in 1600 years = 0

Odd days in 300 years = 1

80 years = (60 ordinary years + 20 leap year) = (60 x 1 + 20 x 2)= 2 odd days

Jan = 25 days = (3 weeks + 4 days) = 4 odd days.

Total number of odd days = (0 + 1 + 2 + 4) = 7= 0 odd day.

Given day is Sunday.