Aptitude - Calendar - Discussion

First day of any century eg 21 century is 01/01/2001 and not 01/01/2000 and first day of century can start either Monday Tuesday Thursday and Saturday.

Thus last day of century can be Sunday Monday Wednesday and Friday as explained by many which I agree.

But first day of 1stcentury century 01/01/0001 or 1st day of AD1 is a Sunday is that an exception? And the one who need why 100? Is not a leap year here it goes?

Actually a year contains 365.24237 days thus to make up 365.25 first we have one day extra after every forth year to make up the average then to make it. 01 less we do not have multiple of 100 as leap year so average bounces to 365.24 now to make more precise or to make 365.2425 we have then every multiple of 4000 as a leap year.

We can even make it more precise by not having leap year on 4000 otherwise we end up with one day advance by 8000 years but that is not done cause earths revolution speed or say velocity is decreasing it is descending but with a very slow rate which will make greater effect by then.

No, this is wrong: because the day on 31st December 1799 was a Tuesday (So last day of century can be a Tuesday as of 17th century last day was Tuesday).

No. Off odd days in 100 years = 5;
But only from 1601 to 1700 (as 1700 is divisible by 4 but not by 400 hence not leap year) BUT No. Off odd days in 100 years = 6 from 1600 to 1699 (as 1600 is a leap year so 25 leap years and 75 normal so 6 odd days).

Hence: The last days are Friday + 6 odd days = Thursday (6odd days because the here year 1400, 1600, 2000 is considered).

Thursday + 5 odd days = Tuesday.

Tuesday + 5 odd days = Sunday.

Sunday + 5 odd days = Friday.

For confirmation please check actual days: the day on 31st December 1599 is Friday; a day on 31st December 1699 is Thursday; a day on 31st December 1799 is Tuesday; day on 31st December 1899 is Sunday; a day on 31st December 1999 is Friday.

In 100years there is 24 leap years & 76 ordinary years
(100 is not a leap year )
from 101 to 200years there is 24 leap years & 76 ordinary years (200 is not a leap year)
from 201 to 300years there is 24 leap years & 76 ordinary years
(300 is not a leap year)
form 301 to 400years there is 25 leap years & 75 ordinary years
(400 is a leap year)
from 401 to 500years there is 24 leap years & 75 ordinary years
(500 is not a leap year)
so in 500 years there is 121 leap years and 379 ordinary years
121*2=242 & 379*1=379 Then 379+242=621
For calculate odd days divide 621 by 7,
(621/7)=Quotient 88 & Remainder 5
we have to take only the remainder for odd days
I think u understood

If 01.01.0001 is a Sunday then the last day of the century i.e. 31.12.0001 would be Thursday (A century has 5 odd days).

01.01.0101 would be Friday and the last day of this century year would be Tuesday.

01.01.0201 would be Wednesday and last day of this century would be Sunday.

01.01.0301 would be Monday and last day of this century i.e. 31.01.0400 would be a Saturday.

Again 01.01.0401 would be a Sunday.

Thus we see that the last day of century years are Tuesday or Thursday or or Saturday or Sunday.

Please correct me if my calculation is wrong.

The earth takes 365.24 days to take one revolution about sun. So after 4 year a correction of 1 day is taken for extra 0.98 day.

And to correct an error of 0.02 day 100th year is not taken as leap year. After a Century that error is a full day long, so we skip the leap year.

This is easy to understand when you realize the difference between 365.25 and 365.24 is 1/100 of a day per year. So after 100 years we have accumulated a full day of error.

Hi Friends,
century year ending day
100 - 5 odd days - friday
200 - 3 odd days - wednesday
300 - 1 odd day - monday
400 - 0 odd day - sunday
500 - 5 odd days - friday
600 - 3 odd days - wednesday
700 - 1 odd day - monday
800 - 0 odd day - sunday
So it will repeating and so on...
therefore the year ending day cannot be Tuesday, Thursday, Saturday.So this is the final answer.

We all know that every ordinary has both last and first day same
And in a leap year the last day is the next of first day,
So any one can explain that the first day cannot be Wednesday ?

100 - 5 odd days - friday
200 - 3 odd days - wednesday
300 - 1 odd day - monday
400 - 0 odd day - sunday
500 - 5 odd days - friday
600 - 3 odd days - wednesday
700 - 1 odd day - monday
800 - 0 odd day - sunday

We can easily check the following table

Century year Ending Day

1300 Sunday
1400 Saturday
1500 Friday
1600 Thursday
1700 Wednesday
1800 Tuesday
1900 Monday
2000 Sunday

Every day of the week gets covered at the end of each century. Plus, if this century ends on a day 'd', next will end on the day 'd-1' & so on.

So, either the options are wrong or I am missing some vital point.

As per the given solution, if we calculate, then we get:

100 - 5 odd days - friday
200 - 3 odd days - wednesday
300 - 1 odd day - monday
400 - 0 odd day - sunday
500 - 4 odd days - Thursday
600 - 2 odd days - Tuesday
700 - 0 odd day - Sunday
800 - 0 odd day - Sunday.

I guess ideally the answer here should be none of these. Am ai right? Please, anyone explain me.

The question is to find the one that not end with a century then we need to find which days will end with a century.

100/7 = (remainder 2 therefore Monday)
200/7 = (rem 4 therefore wed)
300/7(rem 6 therefore Friday)
400/7 = (rem 0 so Saturday)

Tuesday the only one day given in the options which don't end in a century.

I hope it was easy to understand.