Introduction / Context:
This problem checks your comfort with counting days forward and backward across months and into the next year. Starting from a given weekday for 12 February 1986, we are asked to find the weekday on 1 January 1987. The question uses the fact that years can be leap or non leap and that the arrangement of days repeats every 7 days.
Given Data / Assumptions:
- 12 February 1986 is a Wednesday.
- We must find the day of the week on 1 January 1987.
- Year 1986 is not a leap year.
- We assume the Gregorian calendar.
Concept / Approach:
We can work either forward from 12 February 1986 to 1 January 1987 or backward from 1 January 1987 to 12 February 1986. The easiest approach is to count how many days remain in 1986 after 12 February, then convert that total into a number of days modulo 7 to find the weekday shift at the end of the year. From there, we determine the weekday for 1 January 1987 using the weekly cycle pattern.
Step-by-Step Solution:
Start from 12 February 1986 (Wednesday).
Days remaining in February after 12 February: February has 28 days in 1986, so remaining days = 28 - 12 = 16 days.
From March to December 1986, the months contribute:
March: 31, April: 30, May: 31, June: 30, July: 31, August: 31, September: 30, October: 31, November: 30, December: 31.
Total days from March to December = 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 = 306 days.
Total days from 13 February 1986 up to and including 31 December 1986 = 16 + 306 = 322 days.
Odd days in 322 = 322 mod 7 = 0, because 7 * 46 = 322.
Thus, 31 December 1986 falls on the same weekday as 12 February 1986, which is Wednesday.
Therefore, 1 January 1987, which is the next day after Wednesday, must be Thursday.
Verification / Alternative check:
If 31 December 1986 is Wednesday, then the weekly sequence around year end is:
Wednesday (31 December 1986), Thursday (1 January 1987), Friday (2 January 1987), and so on.
This is consistent with our calculation of zero odd days between 12 February and 31 December.
Why Other Options Are Wrong:
Option A (Wednesday): Would make 1 January 1987 the same day as 31 December 1986, which is impossible.
Option B (Tuesday): Would require a shift of 6 days backward rather than 1 forward.
Option D (Friday): Would require two days forward, not one.
Option C (Thursday): Correct, because 1 January 1987 is one day after Wednesday.
Common Pitfalls:
A typical error is miscounting the days left in February or forgetting whether the year is a leap year.
Some candidates incorrectly include the starting day in the count or double count the last day.
Another mistake is to forget to reduce the total by taking modulo 7 and instead trying to track the weekday after every month mentally, which is error prone.
Final Answer:
1 January 1987 falls on a Thursday.
Discussion & Comments