Mathematical Aptitude - Calender Questions

6. If the first day of the ordinary year (other than the leap year) was Friday, then which was the last day of that year?

  • Option : C
  • Explanation : An ordinary year has 365 days. Week starting with Friday will end in Thursday. Hence, the 364th day (end of complete 52 weeks) will be Thursday. The 365th day will be Friday. Thus, the first and last day of an ordinary year are same.
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7. It was Monday on January 1, 2007. What was the day of the week on January 1, 2011?

  • Option : B
  • Explanation : Odd days in 2007 = 1 (2007 is an ordinary year and we are doing calculation from January 1)
    Odd days in 2008 = 2 (2008 is a leap year)
    Odd days in 2009 = 1 (ordinary year)
    Odd days in 2010 = 1 (ordinary year)
    Thus, January 1, 2011, will be Monday plus 5 days, i.e., Saturday.
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8. If the fourth Saturday of a month is the 22nd day, then what day is the 13th day of the month?

  • Option : C
  • Explanation : The earlier three Saturdays are on 15th, 8th and 1st. If 15th is Saturday and hence, Thursday falls on 13th. Thus, 13th is Thursday.
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9. The year next to 1991 will have the same calendar as that of the year 1991.

  • Option : D
  • Explanation : There are two conditions for two years having the same calendar: both having same length in terms of number of days and first day starting with same day of the week.
    The year 1991 has 365 days, that is, 1 odd day, and year 1992 has 366 days, that is, 2 odd days, while year 1993 has 365 days, that is, 1 odd day. The years 1994,1995, and 1996 have 1 odd day each.
    The sum of odd days so calculated from year 1991 to 1996.
    (1 + 2 + 1 + 1 + 1 + 1) = 7 odd days.
    Hence, the year 1997 will have the same calendar as that of the year 1991.
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10. What day of the week was May 28, 2007?

  • Option : D
  • Explanation : 28th May, 2007 = (2000 years + 6 years + period from 1.1.2007 to 28.5.2007)
    Odd days in 2000 years = 0
    Odd days till 2006 = (5 ordinary years + 1 leap year) =(5 × 1 + 1 × 2) = 7 odd days

    JanFebMarchAprilMayTotal
    3128313028148
    148 days = (21 weeks + 1 day) ⇒ 1 odd day
    Total number of odd days = (2000 years + 6 years + period from 1.1.2007 to 28.5.2007)
    = (0 + 7 + 1) = 8 odd days, i.e., again 1 odd day. Hence, Monday is the answer.
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