Calendar All Reasoning Aptitude

To determine the day of the week for 15 August 2013, 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 2013 and a reference date with a known day of the week. Let's choose 1 January 2013, which was a Tuesday.

The number of days between 1 January 2013 and 15 August 2013 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) = 247 days

247 divided by 7 gives a remainder of 2. This means that there are 2 odd days between 1 January 2013 and 15 August 2013.

Since 1 January 2013 was a Tuesday, going forward 2 odd days (2 days forward) from Tuesday, we get:

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

Therefore, 15 August 2013 was a Thursday.

The correct answer is B. Monday.

If 1 January 2018 was a Monday, then 31 December 2018 would also be a Monday. This is because the year 2018 is not a leap year, so it has 365 days, which is exactly 52 weeks and 1 day. This means that after 52 weeks, we will be back to the same day of the week as 1 January 2018, which is Monday. The additional 1 day will take us one day forward from Monday, which is Tuesday. Therefore, 31 December 2018 is a Monday.

The correct answer is A. Saturday.

We can determine the day of the week for 26 February 2005 by calculating the odd days between 29 January 2003 and 26 February 2005.

• Odd days between 29 January 2003 and 29 January 2004:

  • Number of days = 365 (2003 is not a leap year)
  • Odd days = 365 % 7 = 1

• Odd days between 29 January 2004 and 29 January 2005:

  • Number of days = 366 (2004 is a leap year)
  • Odd days = 366 % 7 = 2

• Odd days between 29 January 2005 and 26 February 2005:

  • Number of days = 28 (January) + 26 (February) = 54
  • Odd days = 54 % 7 = 5

Total odd days between 29 January 2003 and 26 February 2005 = 1 + 2 + 5 = 8

Since 29 January 2003 was a Wednesday, going forward 8 odd days (8 days forward) from Wednesday, we get:

• Wednesday + 1 odd day = Thursday
• Thursday + 1 odd day = Friday
• 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, 26 February 2005 was a Saturday.

The correct answer is C. Sunday.

To determine the day of the week for 14 March 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 14 March 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 14 March 2010 is:

(31 days in January) + (28 days in February) + (14 days in March) = 73 days

73 divided by 7 gives a remainder of 3. This means that there are 3 odd days between 1 January 2010 and 14 March 2010.

Since 1 January 2010 was a Friday, going forward 3 odd days (3 days forward) from Friday, we get:

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

Therefore, 14 March 2010 was a Sunday.

To determine the day of the week for 26 January 2012, 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 26 January 2012 and a reference date with a known day of the week. Let's choose 1 January 2012, which was a Sunday.

The number of days between 1 January 2012 and 26 January 2012 is:

26 days

26 divided by 7 gives a remainder of 5. This means that there are 5 odd days between 1 January 2012 and 26 January 2012.

Since 1 January 2012 was a Sunday, going forward 5 odd days (5 days forward) from Sunday, we get:

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

Therefore, 26 January 2012 was a Thursday.

The correct answer is A. Tuesday.

We can determine the day of the week for 17 October 2000 by calculating the odd days between 18 October 2006 and 17 October 2000.

• Odd days between 18 October 2006 and 18 October 2000:
  • Number of days = 6 years
  • Odd days for non-leap years = 1 odd day per year
  • Odd days for leap years = 2 odd days per year

In the given period, there is one leap year (2004), so we have 5 ordinary years and 1 leap year. Therefore, the total odd days between 18 October 2006 and 18 October 2000 are:

Total odd days = (5 ordinary years * 1 odd day per year) + (1 leap year * 2 odd days per year) = 5 + 2 = 7 odd days

Since 7 is a multiple of 7, it doesn't affect the day of the week. So, 18 October 2000 will also be a Wednesday.

Now, to find the day of the week for 17 October 2000, we need to go back 1 day from Wednesday:

• Wednesday - 1 day = Tuesday

Therefore, 17 October 2000 was a Tuesday.