Mathematical Aptitude - Calender Questions

11. What was the day of the week on 16 June, 1999?

  • Option : C
  • Explanation : 16th June, 1999 = (1900 years + 98 years + period from 1.1.1999 to 16.6.1999)
    Now first deal with 1998 complete years; then how many odd days are there in 1998 years?
    Odd days in 1600 years = 0
    Odd days in 300 years = (5 × 3) = 1
    98 years have 24 leap years + 74 ordinary years. Number of odd days in 98 years (24 × 2 + 74) = 122 = 3 odd days.
    Now come to calculation of odd days in period from 1.1.1999 to 16.6.1999.
    MonthsJanFebMarchAprilMayJuneTotal
    Odd Days312831303116167
    167 days = 23 complete weeks plus 6 odd days (this result is obtained by dividing 167 days by 7).
    Total number of odd days = (0 + 1 + 3 + 6) = 10 ⇒ 3 odd days
    Thus, the day asked in the question is Wednesday
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12. What will be the day of the week on 16 August, 2010?

  • Option : B
  • Explanation : 16 August, 2010 = (2000 + 9 years + period 1.1.2010 to 16.8.2010)
    Odd days in 2000 years = 0
    9 years = (2 leap years + 7 ordinary years) = (2 × 2 + 7 × 1) = 11 odd days
    11 can be divided by 7 ⇒ 4 odd days
    MonthsJanFebMarchAprilMayJuneJulyAugTotal
    Odd Days3128313031163116228
    The odd days can be calculated for each month separately and then added up. This can save some time in calculation. Such as January has 3 odd days (31 divided by 7 gives remainder of 3 and so on).
    Now, 228 days = 32 complete weeks + 3 extra days, it means 3 odd days.
    Total number of odd days = (0 + 0 + 4 + 4) = 8; it means 1 odd day.
    Thus, 16 August, 2010 was Monday.
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13. It was Wednesday on 15 August 2012. What should be the day on November 15, 2013?

  • Option : C
  • Explanation : From August 15, 2012, till August 15, 2013, there is one extra day. In the rest of 16 days of August, there are 2 odd days. In September, there are 2 odd days, and in October, 3 odd days. In first 15 days of November, there will be 1 odd day. Thus, the total number of odd days is 1 + 2 + 2 + 3 + 1 = 9; it means 2 extra (odd) days. Hence, November 15, 2013 was Friday.
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14. If it is Sunday today, then what will be the day after 60 days?

  • Option : B
  • Explanation : Each day of the week is repeated after 7 days. Assuming that first day is Sunday, 8, 15, 22, 29, 36, 43, 50 and 57 days will be Sundays. Hence, day 58 is Monday, 59 is Tuesday, 60 is Wednesday. Hence, day after 60 days will be Thursday.
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15. If 22 April 2013 is Monday, then what was the day of the week on April 22, 2012?

  • Option : A
  • Explanation : The year 2012 is a leap year. Thus, it has 2 odd days.
    But as calculation is to be done from April 22, 2012, till April 22, 2013, so it has 1 odd day only. As the calculation is to be done backwards, thus April 22nd was one day less. Thus, it was Sunday.
    Note: Had the question been about April 22, 2014, the answer would have been Tuesday. If the same question is framed for April 22, 2016, the answer would have been Friday, as 2016 is a leap year.
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