Question

What was the day of the week on 30 Sep 2010?

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

Hint:

Code for odd days: Sun(0), Mon(1), Tue(2), Wed(3), Thu(4), Fri(5), Sat(6). Remember multiples of 400 years have 0 odd days.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to calculate the exact day of the week for the given date: September 30, 2010.
Step 2: Detailed Explanation:
Let's count the number of odd days up to Sep 30, 2010. 1. Odd days in completed years (up to 2009):

2000 years: 0 odd days.
Remaining 9 years (2001 to 2009):
Leap years in this period (2004, 2008): 2.
Ordinary years: \(9 - 2 = 7\).
Odd days from years: \((2 \times 2) + (7 \times 1) = 4 + 7 = 11\).
\(11 \pmod 7 = 4\) odd days.
2. Odd days in the year 2010 (up to Sep 30):

Jan (31): 3
Feb (28): 0 (2010 is not a leap year)
Mar (31): 3
Apr (30): 2
May (31): 3
Jun (30): 2
Jul (31): 3
Aug (31): 3
Sep (30): \(30 \pmod 7 = 2\)
Total for months: \(3+0+3+2+3+2+3+3+2 = 21\).
\(21 \pmod 7 = 0\) odd days.
3. Total Odd Days: \[ 4 (\text{from years}) + 0 (\text{from months}) = 4 \] 4. Finding the Day:

0 = Sunday
1 = Monday
2 = Tuesday
3 = Wednesday
4 = Thursday
Step 3: Final Answer:
The day was Thursday.