If 30th January 2003 was a Thursday, then what day of the week fell on 2nd March 2003?

Introduction / Context:
This calendar-based reasoning question asks you to determine the day of the week on a target date, given the day on a reference date. You must carefully count the number of days between the two dates, taking into account the lengths of the months, and then use modular arithmetic to find the resulting day of the week.

Given Data / Assumptions:

- 30th January 2003 was a Thursday.- We need the day of the week on 2nd March 2003.- The year 2003 is not a leap year, so February has 28 days.

Concept / Approach:
The basic idea is to count how many days lie between 30th January and 2nd March, then move forward that many steps in the weekly cycle starting from Thursday. Since a week has 7 days, we only need the remainder when the total number of days is divided by 7. This remainder tells us how many days ahead the target day is from the reference day.

Step-by-Step Solution:
Step 1: From 30th January to 31st January, there is 1 day.Step 2: February 2003 has 28 days because 2003 is not divisible by 4.Step 3: From 1st February to 28th February, there are 28 days.Step 4: From 1st March to 2nd March, there are 2 days.Step 5: Total days between 30th January and 2nd March (exclusive of the starting date, inclusive of the ending date) equals 1 + 28 + 2 = 31 days.Step 6: Now find 31 divided by 7. We get 31 = 7 * 4 + 3, so the remainder is 3.Step 7: A remainder of 3 means 2nd March is 3 days ahead of Thursday in the weekly cycle.Step 8: Count forward: Thursday to Friday (1), Friday to Saturday (2), Saturday to Sunday (3). So 2nd March 2003 falls on Sunday.

Verification / Alternative check:
We can cross-check by listing a shorter chain of dates. 30th January is Thursday, so 31st January is Friday. Then 7th February is also Friday, 14th February is Friday, 21st February is Friday and 28th February is Friday. That means 1st March is Saturday and 2nd March is Sunday. This alternative method confirms the same result without using formal modular arithmetic.

Why Other Options Are Wrong:
Thursday would imply that the number of days between the dates is a multiple of 7, which is not true for 31 days. Tuesday and Saturday correspond to remainders of different sizes when dividing by 7 and do not match the actual count of 31 days. Only Sunday is three days ahead of Thursday and therefore correct.

Common Pitfalls:
Errors often arise from miscounting the days in February or including the starting date incorrectly. Some students also forget to calculate the remainder when dividing by 7 and instead try to track every day, which is more time-consuming and error prone. Being systematic about month lengths and remainders greatly reduces such mistakes.

Final Answer:
The day of the week on 2nd March 2003 was Sunday.