If 26th January, 2019 was a Saturday, what day of the week would it have been on the 15th of August, 2015?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Saturday
The weekday repeats every 7 days, so only the odd days, the days left over after whole weeks, change it. Counting the days from 15 August 2015 to 26 January 2019 and taking out whole weeks shows how far the weekday moves; a leap year has 366 days, 2 odd days, and an ordinary year 365 days, 1 odd day.
The three whole years (a leap year gives 2 odd days, an ordinary year 1):
15 Aug 2015 to 15 Aug 2016: 366 days (it includes 29 February 2016), 2 odd days
15 Aug 2016 to 15 Aug 2017: 365 days, 1 odd day
15 Aug 2017 to 15 Aug 2018: 365 days, 1 odd day
The part year (15 Aug 2018 to 26 Jan 2019):
16 (rest of August) + 30 + 31 + 30 + 31 + 26 = 164 days
164 days \(=23\) weeks + 3 days, 3 odd days
All the odd days (whole weeks taken out):
Total odd days \(=2+1+1+3=7\), which is one whole week, 0 odd days
So 15 August 2015 fell on the same weekday as 26 January 2019, a Saturday.