In a month of 31 days, the dates of all the Wednesdays add up to 75. On which day of the week does the 20th of that month fall?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Monday
The same weekday comes back every 7 days, so if the first Wednesday is the \(d\)th, the Wednesdays are \(d\), \(d+7\), \(d+14\), \(d+21\) and, if it fits in the month, \(d+28\). A month has either 4 or 5 Wednesdays.
With 4 Wednesdays: \(4d+42=75\) gives \(4d=33\), not a whole number, so this is impossible
With 5 Wednesdays: \(5d+70=75\) gives \(d=1\)
Wednesdays are the 1st, 8th, 15th, 22nd and 29th (sum \(=75\))
The 20th is \(20-15=5\) days after Wednesday the 15th: Thursday, Friday, Saturday, Sunday, Monday
