Introduction / Context:
This question asks you to identify all the dates in a specific month and year that fall on a particular weekday. Here, we are dealing with Mondays in July 2004. Such problems test your understanding of how weekdays progress through a month once you know the weekday for the first day of that month or for some reference date in that year.
Given Data / Assumptions:
- Month: July, Year: 2004.
- We must find all dates in July 2004 that were Mondays.
- We are using the Gregorian calendar.
- Year 2004 is a leap year.
Concept / Approach:
The pattern of weekdays in a month repeats every 7 days. Once we know the weekday for 1 July 2004, we can add 7 repeatedly to find all dates in that month with the same weekday. One way is to use a known reference date within 2004 and count forward; another is to use a standard calendar algorithm. After identifying the weekday of 1 July, we add multiples of 7 to locate all Mondays in that month.
Step-by-Step Solution:
From a verified calendar source or by calculation, 1 July 2004 was a Thursday.
Therefore, the weekdays for the first few dates of July 2004 are:
1 July: Thursday, 2 July: Friday, 3 July: Saturday, 4 July: Sunday.
5 July: Monday.
Since weekdays repeat every 7 days, every date obtained by adding 7 to 5 will also be a Monday.
So the Mondays in July 2004 are 5, 5 + 7 = 12, 12 + 7 = 19, and 19 + 7 = 26.
Thus, the Mondays are on 5th, 12th, 19th and 26th July 2004.
Verification / Alternative check:
Confirm that none of these dates exceed the length of the month. July has 31 days, so all these dates are valid.
We can also quickly list the full sequence to cross check: Monday on 5, 12, 19, 26, and then 2 August would be the next Monday.
No other dates in July 2004 will be Monday, since inserting any other number breaks the plus 7 pattern.
Why Other Options Are Wrong:
Option A (6th, 10th, 21st, 30th): The pattern does not maintain a gap of 7 days between all dates.
Option B (12th, 7th, 19th, 28th): Not in increasing order and still not a clean plus 7 pattern.
Option C (5th, 10th, 24th, 17th): Again breaks the regular 7 day spacing required for the same weekday.
Option D (5th, 12th, 19th, 26th): Correct, following the regular Monday pattern through the month.
Common Pitfalls:
Some learners try to guess dates without establishing the weekday of the first of the month.
Forgetting that the same weekday repeats every 7 days leads to irregular and incorrect sequences.
Confusing July with June or August when checking month lengths can also cause mistakes.
Final Answer:
In July 2004, Monday fell on 5th, 12th, 19th and 26th.
Discussion & Comments