Consider the following statements.
I. If 1st March of a year is a Monday, then 1st June of that year is a Tuesday.
II. If 10th January of a leap year is a Sunday, then 10th March of that year is a Wednesday.
III. If 1st January of a leap year is a Saturday, then that year has 53 Saturdays and 53 Sundays.
Which of the above statements are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → I and III only
Count the odd days month by month: a month of 31 days gives 3, of 30 days 2, February 0 in an ordinary year and 1 in a leap year. A leap year has 366 days = 52 weeks + 2 days.
I. If 1st March of a year is a Monday, then 1st June of that year is a Tuesday. Correct.
Days from 1st March to 1st June: March 31 + April 30 + May 31 \(=92\)
Odd days: \(3+2+3=8=7+1\), so 1 odd day
Monday \(+\) 1 \(=\) Tuesday
II. If 10th January of a leap year is a Sunday, then 10th March of that year is a Wednesday. Incorrect.
10th January to 31st January: 21 days, 0 odd days
February of a leap year: 29 days, 1 odd day
1st March to 10th March: 10 days, 3 odd days
Total \(=0+1+3=4\) odd days: Sunday \(+\) 4 \(=\) Thursday, not Wednesday (Wednesday would need an ordinary year)
III. If 1st January of a leap year is a Saturday, then that year has 53 Saturdays and 53 Sundays. Correct.
\(366=52\times7+2\): 52 full weeks plus 2 extra days
The 2 extra days are the same weekdays as 1st and 2nd January: Saturday and Sunday
So Saturday and Sunday each occur \(52+1=53\) times