Calendar - Aptitude MCQ Questions and Solutions with Explanations

Odd days ⇒ The number of days more than complete number of weeks in the given period are odd days.
123 = 7 × 17 + 4 ⇒ 4 odd days.

After every 400 years, the same day occurs. (Because a period of 400 years has 0 odd days)
Thus, 18^th April 1603 is Thursday, After 400 years i.e., on 18^th April 2003 has to be Thursday.

$$\frac{{126}}{7}$$ = 0
Each day of the week is repeated after 7 days.
So, after 126 days, it will be Friday.
After 126 days, it will be Friday

Given that 25th August = Thursday
Hence 29th August = Monday
So 22nd,15th and 8th and 1st of August also will be Mondays
Number of Mondays in August = 5

In 400 consecutive years there are 97 leap years. Hence, in 400 consecutive years February has the 29th day 97 times and the remaining eleven months have the 29th day 400 × 11 or 4400 times.
Thus the 29th day of the month occurs
= 4400 + 97
= 4497 times.

Mentioned month begins on a Saturday and has 30 days
Sundays = 2^nd, 9^th, 16^th, 23^rd, 30^th
⇒ Total Sundays = 5
Every second Saturday is holiday.
1 second Saturday in every month
Total days in the month = 30
Total working days = 30 - (5 + 1) = 24

We know every year has 1 odd days
We know leap year has 2 odd days
Here, Number of Normal years= 22 and number of Leap years =8
So odd days =22+16 =38 i.e 3 odd days (remainder when 38 is divided by 7,i.e. 3)

Hence, it was a Thursday.

1^st Jan 1901 = (1900 years + 1^st Jan 1901)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)
Number of odd days in the period 1601 - 1900
= Number of odd days in 300 years
= 5 x 3 = 15 = 1
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
1^st Jan 1901 = 1 odd day
Total number of odd days = (0 + 1 + 1) = 2
2 odd days = Tuesday
Hence 1 January 1901 is Tuesday.

This is a leap year.
So, none of the next 3 years will be leap years.
Each ordinary year has one odd day, so there are 3 odd days in next 3 years.
So the day of the week will be 3 odd days beyond Wednesday i.e. it will be Saturday

Given that January 1, 2004 was Thursday.
Odd days in 2004 = 2 (because 2004 is a leap year)
(Also note that we have taken the complete year 2004 because we need to find out the odd days from 01-Jan-2004 to 31-Dec-2004, that is the whole year 2004)
Hence January 1, 2005 = (Thursday + 2 odd days) = Saturday