The birthday of Gurkiran falls on Sunday 21 May of a certain year. In the same year, on which day of the week will the birthday of Shreyas fall if he was born on 14 November?

Difficulty: Medium

Correct Answer: Tuesday

Explanation:


Introduction / Context:
Here you must determine the weekday for a later date in the same year, given the weekday for an earlier birthday. This time the gap between the two dates is several months, from May to November, so you need to handle multiple month lengths and still convert the total days into a weekday shift.


Given Data / Assumptions:

  • Gurkiran has a birthday on Sunday 21 May.
  • Shreyas has a birthday on 14 November of the same year.
  • Month lengths: May 31, June 30, July 31, August 31, September 30, October 31, November 30.
  • The year is treated as a standard non leap year for month lengths.


Concept / Approach:
The weekday difference depends on the total number of days between 21 May and 14 November. We count the days month by month, take the total modulo 7 to get odd days, and then shift the weekday of 21 May forward by that many odd days to find the weekday of 14 November.


Step-by-Step Solution:
Step 1: Days remaining in May after 21 May are 31 - 21 = 10 days. Step 2: Full months between June and October: June 30, July 31, August 31, September 30, October 31. Step 3: Sum these days: 10 (end of May) + 30 + 31 + 31 + 30 + 31 = 163 days up to 31 October. Step 4: Now count days in November from 1 November to 14 November inclusive, which gives 14 days. Step 5: Total days from 21 May to 14 November = 163 + 14 = 177 days. Step 6: Compute odd days: 177 divided by 7 gives remainder 2 because 177 = 7 * 25 + 2. So the weekday advances by two days from Sunday to Tuesday.


Verification / Alternative check:
To verify, you could move in smaller steps, for example from 21 May to 21 June, then to later months, always keeping track of odd days. Eventually you will still accumulate 177 days, or 2 odd days, between the two birthdays. Starting at Sunday and moving forward first to Monday, then to Tuesday confirms that 14 November is a Tuesday.


Why Other Options Are Wrong:
Wednesday: This would correspond to three odd days, not two.

Friday: This is four days ahead of Sunday and does not match the computed remainder.

Saturday: This is six days ahead of Sunday, again inconsistent with our two day shift.


Common Pitfalls:
When working over many months, students often make mistakes in month lengths or forget to include the correct number of days at the beginning or end of the interval. It is safer to write each step clearly and double check the arithmetic before converting to odd days.


Final Answer:
Therefore, the birthday of Shreyas on 14 November falls on Tuesday in that same year.

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