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Math Help - day of month

  1. #1
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    day of month

    first day of 1999 is sunday.what day is the last day?
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  2. #2
    Super Member Aryth's Avatar
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    This is pretty simple, there's 365 days in a year. Divide 364 (We already know Sunday) by 7, take the remainder and count from Sunday and you'll have your answer:

    \frac{364}{7} = 52 \ remainder \ 0

    The end of the year is also a Sunday. If it is a leap year, it will be the day after that.
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  3. #3
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    Quote Originally Posted by hena View Post
    first day of 1999 is sunday.what is the last day
    I will give you 2 hints:

    (Hint 1)
    1999 wasnt a leap year. So it had 365 days. Sunday repeats for every 7 days.... that is if 1st is a sunday, so is 8th Jan, 15th Jan and so on.....

    (Hint 2)
    365 = 1 + 7 x 52
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  4. #4
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    any other suggestion

    is tat mean the answer is sunday
    but they have not given sunday as an option for me
    the option they given are
    monday,wednesday
    friday,saturday
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  5. #5
    Jen
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    I was wrong.

    Sorry
    Last edited by Jen; May 26th 2008 at 06:27 PM.
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  6. #6
    Super Member Aryth's Avatar
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    It's not monday... If you look at any calendar that has many years recorded on it... All years start and end on the same day of the week, unless it is a leap year, then it ends on the day after.

    You cannot include a day once it has been considered already. If you see it started on Sunday and count a week after that, you get Sunday:

    Sunday...

    Monday... 1
    Tuesday.. 2
    Wednesday... 3
    Thursday. 4
    Friday..... 5
    Saturday. 6
    Sunday... 7

    If you continue this till the end of the year, you get 364 days.

    That means, all years start and end on the same day except on Leap Year.
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  7. #7
    Jen
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    Quote Originally Posted by Aryth View Post
    It's not monday... If you look at any calendar that has many years recorded on it... All years start and end on the same day of the week, unless it is a leap year, then it ends on the day after.

    You cannot include a day once it has been considered already. If you see it started on Sunday and count a week after that, you get Sunday:

    Sunday...

    Monday... 1
    Tuesday.. 2
    Wednesday... 3
    Thursday. 4
    Friday..... 5
    Saturday. 6
    Sunday... 7

    If you continue this till the end of the year, you get 364 days.

    That means, all years start and end on the same day except on Leap Year.
    Oh, you are correct, thank you. The first day of the next year would be a monday. Not the last day of the same year.

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  8. #8
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    so which is rite

    give me a suggestion plz
    can i send the ans as monday???
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  9. #9
    Jen
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    Quote Originally Posted by neha1 View Post
    give me a suggestion plz
    can i send the ans as monday???

    I believe that the first day of the next year would be a Monday, however Aryth was correct every year other than leap years end on the same day.
    So if you question asks what day the next year began on then yes, it would be Monday.
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  10. #10
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    If the number if days in a year was a multiple of 7, then a given day would land on the same weekday every year because the week and year cycles would be aligned. If the year was 7 days long, what would the 8th day be? If they were 14 days long, what would the 15th day land on? The same as the first day, right?

    However,

    365/7 = 52 and 1/7th (i.e. one day longer than 52 weeks)

    366/7 = 52 and 2/7ths (i.e. two days longer than 52 weeks)

    So if, say, in a normal 365 day year, the first day was Tuesday...

    The first 52 weeks would be

    [Tue,Wed,Thu,Fri,Sat,Sun,Mon]

    Then the spare day at the end of the year would be a Tuesday.

    Making the first day of the next year a Wednesday

    If it were a leap year, then you would have 2 spare days after the 52 - Tuesday and Wednesday, making the first day of the next year a Thursday.
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  11. #11
    A riddle wrapped in an enigma
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    And of course, we know that the actual 1st day of 1999 was on a Friday.
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  12. #12
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    Quote Originally Posted by sean.1986 View Post
    If the number if days in a year was a multiple of 7, then a given day would land on the same weekday every year because the week and year cycles would be aligned. If the year was 7 days long, what would the 8th day be? If they were 14 days long, what would the 15th day land on? The same as the first day, right?

    However,

    365/7 = 52 and 1/7th (i.e. one day longer than 52 weeks)

    366/7 = 52 and 2/7ths (i.e. two days longer than 52 weeks)

    So if, say, in a normal 365 day year, the first day was Tuesday...

    The first 52 weeks would be

    [Tue,Wed,Thu,Fri,Sat,Sun,Mon]

    Then the spare day at the end of the year would be a Tuesday.

    Making the first day of the next year a Wednesday

    If it were a leap year, then you would have 2 spare days after the 52 - Tuesday and Wednesday, making the first day of the next year a Thursday.

    can u plz make it more clear,its very urgent....
    which option(mon,wed,fri,sat) should i choose among this..plz help me out
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  13. #13
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    Basically, the last and first day of 1999 were the same day.
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  14. #14
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    plz............

    Quote Originally Posted by sean.1986 View Post
    Basically, the last and first day of 1999 were the same day.

    but i told they have not given sunday as an option
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  15. #15
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    There's something wrong with the question, then, because all leap years land on years that are multiples of 4.
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