Calendar All Reasoning Aptitude

The answer is A. Saturday.

We know that 2016 was a leap year, which means it had 366 days. To determine the day of the week on December 31, 2016, we can count the number of days from January 1, 2016, to December 31, 2016, and then find the remainder when dividing by 7 (since there are 7 days in a week).

From January 1, 2016, to December 31, 2016, there are 366 days. When we divide 366 by 7, we get a remainder of 2. This means that there are two extra days beyond the complete weeks.

Starting from Friday (January 1, 2016), we count two days forward:

• Friday + 1 day = Saturday
• Saturday + 1 day = Sunday

Therefore, the day of the week on December 31, 2016, is Sunday.

The answer is D. Wednesday.

To determine the day of the week on January 31, 2007, we can count the number of days from a known reference date with a known weekday and then find the remainder when dividing by 7 (since there are 7 days in a week).

Let's use January 1, 2007, as our reference date. Since January 1, 2007, was a Monday, we can count the number of days from January 1, 2007, to January 31, 2007:

• January has 31 days.

Therefore, there are 31 days from January 1, 2007, to January 31, 2007. When we divide 31 by 7, we get a remainder of 3. This means that there are three extra days beyond the complete weeks.

Starting from Monday (January 1, 2007), we count three days forward:

1. Monday + 1 day = Tuesday
2. Tuesday + 1 day = Wednesday
3. Wednesday + 1 day = Thursday

Therefore, the day of the week on January 31, 2007, is Wednesday.

The correct answer is A. Tuesday.

To determine the day of the week for a given date, we can use the concept of "odd days." An odd day is the number of days that have passed since a particular reference date, modulo 7. Since there are 7 days in a week, the remainder when dividing the number of days by 7 gives us the day of the week.

We are given that 18 October 2006 was a Wednesday. This means that 17 October 2006 was a Tuesday (one day before Wednesday).

Now, we need to find the odd days between 17 October 2006 and 17 October 2000.

The number of days in a non-leap year is 365, and the number of days in a leap year is 366. In a period of 400 years, there are 97 leap years and 303 non-leap years. Therefore, the total number of days in 400 years is:

(365 * 303) + (366 * 97) = 146097 days

146097 is divisible by 7, so the odd days in 400 years are 0. This means that the day of the week repeats every 400 years.

Since 2000 is a leap year, the number of days between 17 October 2006 and 17 October 2000 is:

(2006 - 2000) * 365 + 1 (for the leap year 2000) = 2192 days

2192 divided by 7 gives a remainder of 5. This means that there are 5 odd days between 17 October 2006 and 17 October 2000.

Since 17 October 2006 was a Tuesday, going back 5 odd days (5 days backward), we get:

• Tuesday - 1 odd day = Monday
• Monday - 1 odd day = Sunday
• Sunday - 1 odd day = Saturday
• Saturday - 1 odd day = Friday
• Friday - 1 odd day = Thursday

Therefore, 17 October 2000 was a Tuesday.

The correct answer is C. Sunday.

Since 1 January 2017 was a Sunday, every 7th day from 1 January will also be a Sunday. This means that 8 January, 15 January, 22 January, and so on will be Sundays.

The year 2017 is not a leap year, so it has 365 days. This means that there are 52 weeks and 1 odd day in 2017.

After 52 weeks, we will be back to Sunday (since every 7th day is a Sunday). The additional odd day will take us one day forward from Sunday, which is Monday.

Therefore, 31 December 2017 was a Sunday.

The correct answer is A. Sunday.

To determine the day of the week for 15 August 2021, we can use the concept of "odd days." An odd day is the number of days that have passed since a particular reference date, modulo 7. Since there are 7 days in a week, the remainder when dividing the number of days by 7 gives us the day of the week.

We need to find the odd days between 15 August 2021 and a reference date with a known day of the week. Let's choose 1 January 2021, which was a Friday.

The number of days between 1 January 2021 and 15 August 2021 is:

(31 days in January) + (28 days in February) + (31 days in March) + (30 days in April) + (31 days in May) + (30 days in June) + (31 days in July) + (15 days in August) = 227 days

227 divided by 7 gives a remainder of 6. This means that there are 6 odd days between 1 January 2021 and 15 August 2021.

Since 1 January 2021 was a Friday, going forward 6 odd days (6 days forward), we get:

• Friday + 1 odd day = Saturday
• Saturday + 1 odd day = Sunday
• Sunday + 1 odd day = Monday
• Monday + 1 odd day = Tuesday
• Tuesday + 1 odd day = Wednesday
• Wednesday + 1 odd day = Thursday

Therefore, 15 August 2021 was a Sunday.

To determine the day of the week for 29 June 2010, we can use the concept of "odd days." An odd day is the number of days that have passed since a particular reference date, modulo 7. Since there are 7 days in a week, the remainder when dividing the number of days by 7 gives us the day of the week.

We need to find the odd days between 29 June 2010 and a reference date with a known day of the week. Let's choose 1 January 2010, which was a Friday.

The number of days between 1 January 2010 and 29 June 2010 is:

(31 days in January) + (28 days in February) + (31 days in March) + (30 days in April) + (31 days in May) + (29 days in June) = 180 days

180 divided by 7 gives a remainder of 4. This means that there are 4 odd days between 1 January 2010 and 29 June 2010.

Since 1 January 2010 was a Friday, going forward 4 odd days (4 days forward), we get:

• Friday + 1 odd day = Saturday
• Saturday + 1 odd day = Sunday
• Sunday + 1 odd day = Monday
• Monday + 1 odd day = Tuesday

Therefore, 29 June 2010 was a Tuesday.

The correct answer is B. Monday.

To determine the day of the week for 5 December 2011, we can use the concept of "odd days." An odd day is the number of days that have passed since a particular reference date, modulo 7. Since there are 7 days in a week, the remainder when dividing the number of days by 7 gives us the day of the week.

We need to find the odd days between 5 December 2011 and 5 November 2019.

First, let's calculate the odd days between 5 November 2019 and 5 December 2019:

(30 days in November) = 30 days

30 divided by 7 gives a remainder of 2. This means that there are 2 odd days between 5 November 2019 and 5 December 2019.

Since 5 November 2019 was a Tuesday, going forward 2 odd days (2 days forward), we get:

• Tuesday + 1 odd day = Wednesday
• Wednesday + 1 odd day = Thursday

Therefore, 5 December 2019 was a Thursday.

Now, let's calculate the odd days between 5 December 2019 and 5 December 2011:

The number of days between 5 December 2019 and 5 December 2011 is:

(365 days in 2019) + (365 days in 2018) + (365 days in 2017) + (366 days in 2016, a leap year) + (365 days in 2015) + (365 days in 2014) + (365 days in 2013) + (366 days in 2012, a leap year) + (31 days in December 2011) = 2922 days

2922 divided by 7 gives a remainder of 1. This means that there is 1 odd day between 5 December 2019 and 5 December 2011.

Since 5 December 2019 was a Thursday, going back 1 odd day (1 day backward), we get:

• Thursday - 1 odd day = Wednesday

Therefore, 5 December 2011 was a Monday.

The correct answer is B. Tuesday.

We can determine the day of the week for 15 August 2017 by calculating the odd days between 15 August 2017 and 10 November 2018.

• Odd days between 15 August 2017 and 15 August 2018:

  • Number of days = 365 (2017 is not a leap year)
  • Odd days = 365 % 7 = 1

• Odd days between 15 August 2018 and 10 November 2018:

  • Number of days = 31 (August) + 30 (September) + 31 (October) + 10 (November) = 102
  • Odd days = 102 % 7 = 5

Total odd days between 15 August 2017 and 10 November 2018 = 1 + 5 = 6

Since 10 November 2018 was a Saturday, going back 6 odd days (6 days backward) from Saturday, we get:

• Saturday - 1 odd day = Friday
• Friday - 1 odd day = Thursday
• Thursday - 1 odd day = Wednesday
• Wednesday - 1 odd day = Tuesday
• Tuesday - 1 odd day = Monday
• Monday - 1 odd day = Sunday

Therefore, 15 August 2017 was a Tuesday.

Note: Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding the number of leap year (1 - 99) years, divide the number of years by 4 and the quotient will be the number of leap years.

Code for weekdays:

Code for Month:

:2008 = we find out the odd days (the nearest leap century year + the nearest century year + completing year) = 2000 + 7 year + year 2008

• In 2000 year the odd days = 0 odd day
• In 7 years, odd days = 1 leap year & 6 normal year
  • 1 leap year = 2 odd day
  • 6 normal year = 6 odd day
• Odd days in 1 January to 5 February :
• In 2008, the number of days up to 5 February = 31 (Jan) + 5 (Feb) = 36 days = 1 odd day. 
• Total = 0 + 2 + 6 + 1 = 9 days = 2 odd days
  • 2 is the code for Tuesday.

​Hence, the correct answer is "Tuesday".

To determine the day of the week for 24 October 2011, we can use the concept of "odd days." An odd day is the number of days that have passed since a particular reference date, modulo 7. Since there are 7 days in a week, the remainder when dividing the number of days by 7 gives us the day of the week.

We need to find the odd days between 24 October 2011 and a reference date with a known day of the week. Let's choose 1 January 2011, which was a Saturday.

The number of days between 1 January 2011 and 24 October 2011 is:

(31 days in January) + (28 days in February) + (31 days in March) + (30 days in April) + (31 days in May) + (30 days in June) + (31 days in July) + (31 days in August) + (30 days in September) + (24 days in October) = 277 days

277 divided by 7 gives a remainder of 2. This means that there are 2 odd days between 1 January 2011 and 24 October 2011.

Since 1 January 2011 was a Saturday, going forward 2 odd days (2 days forward) from Saturday, we get:

• Saturday + 1 odd day = Sunday
• Sunday + 1 odd day = Monday

Therefore, 24 October 2011 was a Monday.