Suppose that July 9, 2013 fell on a Sunday. Based on this assumption and using calendar reasoning, on which day of the week would January 7, 2014 fall?

Introduction:
This question asks us to transfer weekday information from one date (9 July 2013) to another date (7 January 2014), assuming a particular weekday for the first date. Calendar questions of this type are solved by finding the number of days between the two dates and then using the remainder when divided by 7 to determine the change in weekday.

Given Data / Assumptions:
Given: 9 July 2013 is assumed to be a Sunday. We need: Day of the week on 7 January 2014. We treat 2013 as a normal (non-leap) year, which is true.

Concept / Approach:
If we know the day for one date, we can find the day for another by counting the exact number of days between them. Every 7 days the weekday cycles back to the same day. So if the difference in days between the two dates is a multiple of 7, the weekdays will be the same. Otherwise, the weekday will shift forward by the remainder (0 to 6 days).

Step-by-Step Solution:
Step 1: Determine the dates. Start date: 9 July 2013. End date: 7 January 2014. Step 2: Count the days remaining in 2013 after 9 July. From 10 July to 31 July: 22 days. August: 31 days. September: 30 days. October: 31 days. November: 30 days. December: 31 days. Total from 10 July to 31 December = 22 + 31 + 30 + 31 + 30 + 31 = 175 days. Step 3: Add days from 1 January 2014 to 7 January 2014. That is 7 days. Step 4: Total days between 9 July 2013 and 7 January 2014. From 10 July 2013 to 7 January 2014 = 175 + 7 = 182 days. Including the shift from 9 July to 10 July adds 1 more day, so the total gap from 9 July to 7 January is 182 days. Step 5: Reduce modulo 7. 182 ÷ 7 = 26 with remainder 0. So the weekday does not change at all between these dates. Therefore, 7 January 2014 is the same weekday as 9 July 2013, namely Sunday.

Verification / Alternative check:
You can also check quickly that 26 weeks separate the two dates, confirming that 182 days is an exact multiple of 7. Any date separated by an exact number of weeks from a known weekday will fall on the same weekday.

Why Other Options Are Wrong:
Saturday, Monday, Friday, Tuesday: Each of these assumes a non-zero remainder when dividing the day difference by 7. Since the remainder is 0, there is no shift in the weekday, so these options are incorrect.

Common Pitfalls:
A typical error is miscounting the days in the months, especially confusing 30- and 31-day months, or forgetting to include or exclude the start date properly. Another mistake is not reducing the total number of days modulo 7 correctly.

Final Answer:
January 7, 2014 would fall on a Sunday.