Date: May 28, 2006 Split into years and days: (2005 years + Period from 1.1.2006 to 28.5.2006)
⮞ Calculate Odd Days for Years
Odd days in 1600 years = 0 (Since it's a complete multiple of 400)
Odd days in 400 years = 0 (Same reason as above)
For 5 years: (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) = 6 odd days
⮞ Calculate Odd Days for the Given Period (1.1.2006 to 28.5.2006)
Calculate the total number of days from January 1 to May 28:
Jan, Feb, March, April, May - (31 + 28 + 31 + 30 + 28 ) = 148 days
Convert days into weeks and a remaining day: 148 days = (21 weeks + 1 day)
This gives 1 odd day for the given period.
⮞ Total Odd Days
Add the odd days for years and the odd days for the given period: (0 + 0 + 6 + 1) = 7 odd days
⮞ Determine the Day of the Week
Since there are 7 days in a week and the total odd days are 7, there are 0 odd days.
Given day is Sunday.
What was the day of the week on 17th June, 1998?
Correct Answer is (a) Wednesday
Show Explanation
⮞ Breakdown of the Date:
The date is June 17, 1998. We can break this down into two parts: 1997 years and the period from January 1, 1998, to June 17, 1998.
⮞ Odd Days in 1600 Years:
The method starts by looking at the 1997 years. We divide this into chunks of 1600 years. Odd days in 1600 years are 0. This is because the calendar repeats every 400 years, and 1600 is a multiple of 400.
⮞ Odd Days in 300 Years:
The remaining 397 years are divided into chunks of 300 years. Odd days in 300 years are calculated as (5 x 3) + 1 = 16. This accounts for the leap years.
⮞ Odd Days in 97 Years:
From the remaining 97 years, we find the number of leap years (24) and ordinary years (73). The odd days in 97 years are calculated as (24 x 2) + 73 = 121, which is equal to 2 odd days.
⮞ Odd Days in the Given Months:
The period from January 1, 1998, to June 17, 1998, is considered. Counting the days in January, February, March, April, May, and the 17 days in June gives us a total of 168 days. 168 days are equivalent to 24 weeks, which means 0 odd days.
⮞ Total Odd Days:
Adding up all the odd days obtained from the various steps: 0 + 16 + 2 + 0 = 18.
⮞ Determine the Day of the Week:
The total odd days, which is 18, corresponds to a certain day of the week. Given that Sunday is 0, Monday is 1, Tuesday is 2, and so on, we find that 18 corresponds to Wednesday.
What will be the day of the week on 15th August, 2010?
Correct Answer is (b) Sunday
Show Explanation
⮞ Start with the given date:
August 15, 2010. The task is to find out which day of the week this date falls on.
⮞ Express the date as a sum of years:
Break down the date into years: 2009 years + the period from January 1, 2010, to August 15, 2010.
⮞ Calculate odd days for large units of time:
Odd days in 1600 years = 0 (because 1600 is a multiple of 400, which has 0 odd days).
Odd days in 400 years = 0 (same reasoning as above).
⮞ Calculate odd days for the remaining years (2009 years):
For 9 years, we have 2 leap years and 7 ordinary years.
Leap years have one extra day, so 2 leap years = 2 x 2 = 4 days.
The 7 ordinary years have 7 days.
In total, we have 4 + 7 = 11 odd days.
⮞ Now, consider the period from January 1, 2010, to August 15, 2010:
Count the days in each month up to August 15:
January (31 days) + February (28 days) + March (31 days) + April (30 days) + May (31 days) + June (30 days) + July (31 days) + August (15 days) = 227 days.
⮞ Convert the days to weeks and remaining days:
227 days can be expressed as 32 weeks (because 7 days make a week) plus 3 days.
⮞ Calculate the total number of odd days:
Add the odd days from the years (11) and the odd days from the period (3), giving a total of 14 odd days.
⮞ Reduce the total odd days to a smaller value:
Since 14 days is equivalent to 2 weeks, the total odd days can be reduced to 0 odd days.
⮞ Determine the day of the week:
If there are 0 odd days, and you know the given date is a Sunday, then the result remains Sunday.
Today is Monday. What day will it be 61 days from today?
Correct Answer is (c) Saturday
Show Explanation
⮞ Cycle of Days:
Imagine a cycle that repeats every 7 days. It's like a weekly pattern where each day of the week has a turn.
⮞ Repeating Pattern:
The days of the week follow a sequence: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, and then it starts again with Monday.
⮞ Counting Days:
If you count 7 days from Monday, you'll reach the next Monday. If you count 14 days, you'll get to the Monday after that. This continues in a regular cycle, with each multiple of 7 bringing you to a new occurrence of the same day.
⮞ Calculating After 63 Days:
Now, think about counting 63 days. Since 63 is a multiple of 7 (9 times 7 equals 63), you would end up on the same day as you started.
⮞ Calculating After 61 Days:
For 61 days, you're a bit short of a full cycle. If you start on a Monday and count 61 days, you would have gone through a few cycles (multiples of 7) and landed on Saturday.
If March 6, 2005, is a Monday, what day of the week was it on March 6, 2004?
Correct Answer is (d) Sunday
Show Explanation
In the year 2004, which is a leap year, there are 2 odd days. However, when we're looking at the period from March 2004 to March 2005, we don't count February 2004. So, for this calculation, there's only 1 odd day.
Now, if March 6th, 2005, is a Monday, that means it's one day ahead of March 6th, 2004. So, March 6th, 2004, was a Sunday, which is one day before Monday.
Which specific dates in April 2001 were Wednesdays?
Correct Answer is (c) 4th, 11th, 18th, 25th
Show Explanation
To find the day on April 1, 2001, we consider the total number of days from the year 1 to that specific date, which is the sum of 2000 years and the period from January 1, 2001, to April 1, 2001.
Calculation Steps:
Odd days in 1600 years = 0 (because multiples of 400 years have 0 odd days)
Odd days in 400 years = 0 (same reason as above)
January + February + March + April (1 day) = (31 + 28 + 31 + 1) = 91 days, resulting in 0 odd days.
Adding up all the odd days gives us a total of 0. Therefore, April 1, 2001, was a Sunday.
In April 2001, Wednesdays occurred on the 4th, 11th, 18th, and 25th. These are the dates when you could mark Wednesdays on the calendar.
How many days are there in y weeks and y days?
Correct Answer is (a) 8y
Show Explanation
To find the total number of days in x weeks and y days, you can use the following formula:
Total days = (x * 7) + y
There are 7 days in a week.
x * 7 gives the total days in x weeks.
Adding y accounts for the remaining days.
So, the total number of days is (x * 7) + y.
but here x=y.
So, (y * 7) + y = 7y + y = 8y.
The last day of a century cannot be _________ .
Correct Answer is (a) Tuesday
Show Explanation
Every century has a certain pattern of odd days, which are the days left over after counting complete weeks. In a century:
The first 100 years have 5 odd days.
The second 100 years have 3 odd days.
The third 100 years have 1 odd day.
The fourth 100 years have 0 odd days.
This pattern repeats for every century.
Now, let's look at the days on which the last day of each century falls:
The last day of the 1st century is Friday.
The last day of the 2nd century is Wednesday.
The last day of the 3rd century is Monday.
The last day of the 4th century is Sunday.
From this pattern, we can deduce that the last day of a century cannot be Tuesday, Thursday, or Saturday.
If February 8th, 2005 fell on a Tuesday, what day of the week was February 8th, 2004?
Correct Answer is (d) Sunday
Show Explanation
The calendar repeats itself every 400 years, and within that cycle, there is a pattern where the days of the week for a given date repeat approximately every 11 years. In the leap year 2004, which has 2 odd days, The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005. Therefore, the day on February 8, 2004, is a Sunday.
Which of the following year will be identical to the year 2007 ?
Correct Answer is (c) 2018
Show Explanation
To find a year identical to 2007, calculate the cumulative odd days from 2007 onwards. Odd days represent the extra days beyond complete weeks in a year. Assign 1 odd day for a normal year and 2 odd days for a leap year.
For the years 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017:
Odd days: 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1
Summing these odd days: 14 odd days = 0 odd days.
Therefore, the calendar for the year 2018 will be identical to the calendar for the year 2007.
Which of the following is not a leap year?
Correct Answer is (a) 900
Show Explanation
Let's check each year:
900: Not a leap year (not divisible by 4).
2000: Leap year (divisible by 4 and 400).
800: Leap year (divisible by 4).
1600: Leap year (divisible by 4, 100, and 400).
Therefore, the year 900 is not a leap year.
The criteria for a year to be a leap year are as follows:
If the year is evenly divisible by 4, it is a leap year.
However, if the year is divisible by 100, it is not a leap year, unless:
The year is also divisible by 400, in which case it is a leap year.
So, the basic rule is divisible by 4, except for years divisible by 100, unless they are also divisible by 400. This rule helps adjust the calendar to account for the fact that the Earth's orbit around the sun takes approximately 365.25 days, and a leap year helps keep our calendars in sync with the astronomical year.
If December 8th, 2007, was a Saturday, what day of the week was December 8th, 2006?
Correct Answer is (a) Friday
Show Explanation
In the Gregorian calendar, the year 2006 is a common or ordinary year, meaning it has 365 days. To determine the day of the week for December 8th, 2006, and December 8th, 2007, we can consider the concept of odd days. An ordinary year has 1 odd day, indicating that each subsequent day in the following year will be one day beyond the corresponding day in the current year.
Starting with December 8th, 2007, which is established as a Saturday, we can deduce that December 8th, 2006, falls one day earlier in the week. Therefore, December 8th, 2006, was a Friday. This conclusion is based on the cumulative effect of the one odd day for an ordinary year, leading to a day-of-the-week shift in the subsequent year.
If 01/01/2008 was a Tuesday, what day of the week was 01/01/2009?
Correct Answer is (b) Thursday
Show Explanation
In the Gregorian calendar, the year 2008 is a leap year, characterized by having 366 days. This results in 2 odd days, considering that a leap year adds an extra day to the calendar. The given information specifies that the 1st day of the year 2008 is a Tuesday.
To determine the day of the week for the 1st day of the year 2009, we take into account the 2 odd days associated with the leap year. As a consequence, the 1st day of the year 2009 is two days beyond Tuesday. Therefore, it can be established that the 1st day of the year 2009 falls on a Thursday. This conclusion is based on the cumulative effect of the leap year's additional odd day, resulting in a day-of-the-week shift in the subsequent year.
If 1st January,2007 was a Tuesday, what day of the week was 1st January,2008?
Correct Answer is (d) Tuesday
Show Explanation
The year 2007 is a non-leap year, consisting of 365 days. In a non-leap year, there is 1 odd day, meaning that the days of the week shift by one day each year. Therefore, if the 1st day of the year 2007 was Monday, the 1st day of the following year, 2008, would be one day beyond Monday. Consequently, it will be Tuesday. This shift occurs due to the fact that 365 is not divisible evenly by 7, resulting in an additional day added to the calendar each year.
