Question

The first and last day
of a month falls on
the same day of the
week. Which of
these years can that
month be in?
2001
2100
2000
2010​

Answer 1

Answer:

6-year pattern: If there is one leap year between dates, the date shall fall on the same day after 6 years

Explanation:

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Answer 2

The year in which this month can be is 2000. (option 3rd)

Given,

The first and last day of a month falls on the same day.

To find,

Which year among the options can that month be in?

Solution,

It can be seen that here, it is given that for a month, the 1st and the last day fall on the same day.

We know that the number of days in most months is either 30 or 31.

While, the month of February can have 28 or 29, based on whether the year is a leap year or not.

28 days: Non-leap year,

29 days: Leap year.

As it is known that the same day repeats after 1 week, or 7 days.

It means the day on the 1st will also be the same as the day on the dates:

8th, 15th, 22nd, and 29th, of any month.

Since, among 30, 31, 28, and, 29, 29 is the only date that can have the same day as the 1st.

And, only the month of February in a leap year can have 29 days.

We know that a normal year divisible by 4, and a century year divisible by 400, will be a leap year.

Among the given options, only 2000 is the leap year.

Thus, a month that is, February, in the year 2000 was having its first and last day on the same day of the week.

Therefore, the year in which this month can be is 2000. (option 3rd)

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