Question:

The birthday of Ms. Y was celebrated six days before Ms. X, who was born on 4th October 1999. The independence day of that year fell on Sunday. On which day did Ms. Y celebrate her birthday, if it was not a leap year?

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Always use modulo arithmetic and count step-by-step when solving calendar problems, ensuring you track each date change carefully.
Updated On: Aug 14, 2025
  • Wednesday
  • Tuesday
  • Monday
  • Sunday
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The Correct Option is B

Solution and Explanation

We are told that Ms. X was born on 4th October 1999.
The year 1999 was not a leap year, and 15th August 1999 (Independence Day) was on a Sunday.
To find the day of the week for 4th October 1999, we count forward from 15th August 1999.
From 15th August to 31st August = 16 days → \(16 \mod 7 = 2\) days ahead of Sunday → Tuesday.
So 31st August 1999 was a Tuesday.
Now, September has 30 days. From 1st September to 30th September = 30 days → \(30 \mod 7 = 2\) days ahead of Tuesday → Thursday.
Thus, 30th September 1999 was a Thursday.
Then 1st October 1999 was a Friday.
2nd October 1999 was a Saturday.
3rd October 1999 was a Sunday.
4th October 1999 was a Monday.
Since Ms. Y’s birthday was 6 days before 4th October, we count backward:
3rd Oct → Sunday
2nd Oct → Saturday
1st Oct → Friday
30th Sep → Thursday
29th Sep → Wednesday
28th Sep → Tuesday
Therefore, Ms. Y’s birthday fell on a Tuesday.
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