Question

If 1st January 2021 was a Friday, what day of the week was 1st January 2022?

• A. Friday
• B. Saturday
• C. Sunday
• D. Monday

Hint:

• A normal year has 365 days, which is 52 weeks + 1 odd day.
• A leap year has 366 days, which is 52 weeks + 2 odd days.
• To find the day of the week for a date in the next year:
  • If the current year (between the two dates) is a normal year, the day shifts forward by 1.
  • If the current year is a leap year (and February 29th of that leap year falls between the two dates), the day shifts forward by 2.
• The year 2021 is not a leap year (2021 is not divisible by 4). So it has 365 days (1 odd day).
• Therefore, 1st Jan 2022 will be one day after 1st Jan 2021 (Friday + 1 = Saturday).

Answer 1

The Correct Option is B

We need to find the day of the week for 1st January 2022, given that 1st January 2021 was a Friday.
Step 1: Determine the number of days between the two dates
The number of days between 1st January 2021 and 1st January 2022 is the number of days in the year 2021.
Step 2: Check if 2021 is a leap year A normal year has 365 days.
A leap year has 366 days.
A year is a leap year if it is divisible by 4, unless it is divisible by 100 but not by 400. Check for 2021: \[ 2021 \div 4 = 505 \text{ remainder } 1 \] So, 2021 is not divisible by 4.
Therefore, 2021 is a normal year. \[ \text{Number of days in 2021} = 365 \] Step 3: Count the odd days Number of odd days in a normal year: \[ 365 \text{ days} = 52 \text{ weeks} \times 7 \text{ days/week} + 1 \text{ day} \] \[ = 364 + 1 \] So, a normal year has 1 odd day.
Step 4: Calculate the day of the week
If a certain date in a normal year is a particular day of the week, the same date in the next year will be that day + 1 (modulo 7).
Given: 1st January 2021 was a Friday.
Since 2021 has 1 odd day, 1st January 2022 will be: \[ \text{Friday} + 1 = \boxed{\text{Saturday}} \]