Calendar Aptitude MCQ Questions with Answers Set 02

Answer: (d) 2015

Explanation:
1. 2009 is an ordinary year, so we need the next ordinary year whose 1 January falls on the same weekday.
2. Odd days: 2009 = 1, 2010 = 1, 2011 = 1, 2012 = 2 (leap), 2013 = 1, 2014 = 1; total = 7 = 0 odd days.
3. So 2015 starts on the same weekday as 2009, and 2015 is also an ordinary year. Hence 2015 repeats the 2009 calendar.

Teacher's Note:
1. Two years share a calendar only if they start on the same weekday AND are both leap or both ordinary.
2. Add the odd days of each year from the given year onward until the total becomes a multiple of 7.

Answer: (b) Saturday

Explanation:
1. From 1 Jan 2009 to 1 Jan 2020 there are 11 full years: 2009 to 2019.
2. Leap years among them: 2012 and 2016 (2 odd days each); the other 9 years give 1 odd day each.
3. Total odd days = 2 x 2 + 9 x 1 = 13; 13 mod 7 = 6.
4. Sunday + 6 days = Saturday.

Teacher's Note:
1. An ordinary year moves a date forward by 1 weekday and a leap year by 2 weekdays.
2. Always reduce the total odd days modulo 7 before counting forward.

Answer: (b) 111

Explanation:
1. 2004 is a leap year, so February has 29 days.
2. January 26 to 31 (both included) = 6 days.
3. Total = 6 (Jan) + 29 (Feb) + 31 (Mar) + 30 (Apr) + 15 (May) = 111 days.

Teacher's Note:
1. When both end dates are included, count the first month's days as (last date - start date + 1).
2. Check whether the year is a leap year before using 28 or 29 days for February.

Answer: (a) Sunday

Explanation:
1. Day after tomorrow = today + 2 = Saturday, so today = Thursday.
2. Yesterday = Wednesday.
3. Three days before Wednesday = Sunday.

Teacher's Note:
1. Convert every phrase into an offset from today (yesterday = -1, day after tomorrow = +2).
2. Add the offsets first, then count once; this avoids step-by-step errors.

Answer: (d) Data inadequate

Explanation:
1. To move from this month into the next month we must know how many days this month has (28, 29, 30 or 31).
2. The question does not say which month it is, so the weekday of the next month's dates cannot be fixed.
3. Hence the data is inadequate.

Teacher's Note:
1. Before calculating, check that every fact needed (month length, leap year) is actually given.
2. Choose 'data inadequate' only after confirming that different valid cases give different answers.

Answer: (d) Fifth Friday

Explanation:
1. Wednesdays fall on 1, 8, 15, 22 and 29 (15th is the third Wednesday).
2. 31st = 29th + 2 days = Friday.
3. Fridays fall on 3, 10, 17, 24, 31, so the 31st is the fifth Friday.

Teacher's Note:
1. Dates with the same weekday differ by multiples of 7 within a month.
2. To find which occurrence a weekday is, list all its dates starting from the earliest in the month.

Answer: (c) Thursday

Explanation:
1. Republic Day is 26th January, which was a Saturday.
2. Saturdays then fall on 2nd, 9th and 16th February.
3. 14th February = 16th February - 2 days = Thursday.

Teacher's Note:
1. Use known fixed dates (Republic Day 26 January, Independence Day 15 August) to anchor the calendar.
2. Jump in steps of 7 to reach a date near the target, then adjust by a few days.

Answer: (b) Friday

Explanation:
1. An ordinary year has 365 days = 52 weeks + 1 day.
2. From 1 January to 31 December is 364 days later, exactly 52 weeks.
3. So the last day has the same weekday as the first day: Friday.

Teacher's Note:
1. In an ordinary year, the first and last days fall on the same weekday.
2. In a leap year, the last day is one weekday after the first day.

Answer: (c) Wednesday

Explanation:
1. October has 31 days, so 1st November is 31 days after 1st October.
2. 31 mod 7 = 3 odd days.
3. Sunday + 3 days = Wednesday.

Teacher's Note:
1. A 31-day month shifts the weekday by 3, a 30-day month by 2.
2. Same date of the next month = this month's odd days added to the weekday.

Answer: (b) Saturday

Explanation:
1. 2008 is a leap year, so February has 29 days.
2. Days from 1 February to 3 March = 29 + 2 = 31 days; 31 mod 7 = 3.
3. Wednesday + 3 days = Saturday.

Teacher's Note:
1. Count the gap in days between the two dates, then take the remainder on division by 7.
2. Remember February 2008 has 29 days because 2008 is divisible by 4.

Answer: (d) Monday

Explanation:
1. 17 Dec 2009 to 17 Dec 2012: the years cross Feb 2010 and Feb 2011 (ordinary, 1 odd day each) and Feb 2012 (leap, 2 odd days), total 4 odd days.
2. So 17 Dec 2012 = Saturday + 4 = Wednesday.
3. 22 Dec 2012 = Wednesday + 5 days = Monday.

Teacher's Note:
1. When moving a date forward by one year, add 2 odd days if a 29 February lies in between, otherwise 1.
2. Shift year by year first, then adjust the date within the month.

Answer: (b) 1, 8, 15, 22, 29

Explanation:
1. Odd days up to 31 Dec 2011: 2000 years give 0; the 11 years 2001-2011 have 2 leap years, so 2 x 2 + 9 x 1 = 13 = 6 odd days.
2. 1 Jan to 1 Apr 2012: Jan 3 + Feb 1 (leap) + Mar 3 + 1 day = 8 = 1 odd day.
3. Total = 6 + 1 = 7 = 0 odd days, so 1 April 2012 was a Sunday.
4. Sundays: 1, 8, 15, 22, 29 April.

Teacher's Note:
1. Odd-day code: 0 = Sunday, 1 = Monday, ..., 6 = Saturday when counting from the start of the calendar.
2. Every multiple of 400 years has 0 odd days, so start counting from the last such year.

Answer: (d) Thursday

Explanation:
1. 15 Aug 2009 to 15 Aug 2109 is exactly 100 years.
2. These 100 years contain 24 leap years (2100 is not a leap year) and 76 ordinary years: 24 x 2 + 76 = 124 = 5 odd days.
3. Saturday + 5 days = Thursday.

Teacher's Note:
1. A century has 5 odd days unless it includes a year divisible by 400 as a leap day.
2. A century year is a leap year only if it is divisible by 400.

Answer: (d) 5th, 12th, 19th, 26th

Explanation:
1. 28 Aug 2008 to 28 Aug 2009 has no 29 February, so 1 odd day: 28 Aug 2009 = Friday.
2. 28 Aug to 28 Dec 2009 = 31 + 30 + 31 + 30 = 122 days = 3 odd days, so 28 Dec 2009 = Monday.
3. The Saturday before is 26 Dec; stepping back by 7 gives 19, 12 and 5 Dec.
4. Saturdays in December 2009: 5th, 12th, 19th, 26th.

Teacher's Note:
1. Shift by whole years first, then by months, using odd days at each step.
2. Once one date's weekday is known, the rest follow by adding or subtracting 7.

Answer: (a) Saturday

Explanation:
1. Today is Sunday, so Laxmi Puja (day after tomorrow) is on Tuesday.
2. Deepawali is on the same day next week, i.e. also a Tuesday.
3. Four days after Tuesday = Saturday.

Teacher's Note:
1. 'Same day next week' means exactly 7 days later, so the weekday does not change.
2. Count forward carefully: four days after Tuesday is Wed, Thu, Fri, Sat.

Answer: (c) Wednesday

Explanation:
1. The desk officer got it and disposed of it on Friday, the same day the senior clerk put it up.
2. The senior clerk acted the day after his leave, so he was on leave on Thursday; the inward clerk forwarded it that day.
3. The inward clerk received it the day before forwarding: Wednesday.

Teacher's Note:
1. For chain-of-events questions, start from the known day and walk backwards one event at a time.
2. Watch words like 'next day' and 'same day' as they decide whether the count moves.

Answer: (b) 2040

Explanation:
1. 2012 is a leap year, so the matching year must also be a leap year (2020 or 2040 among the options).
2. Odd days from 2012 to 2019 = 2+1+1+1+2+1+1+1 = 10 = 3, so 2020 starts on a different weekday.
3. A leap-year calendar repeats after 28 years in this range: 2012 + 28 = 2040.

Teacher's Note:
1. A leap year's calendar normally repeats after 28 years (when no non-leap century year intervenes).
2. An ordinary year's calendar usually repeats after 6 or 11 years, depending on its position in the leap cycle.

Answer: (d) 2

Explanation:
1. Odd days are the days left over after complete weeks.
2. 998 = 12 x 83 + 2.
3. So there are 83 weeks and 2 odd days.

Teacher's Note:
1. Odd days = remainder when the number of days is divided by the number of days in a week.
2. The same idea works for any imaginary week length, not just 7.

Answer: (a) Sunday

Explanation:
1. Between 18 Feb 2005 and 18 Feb 2007 there is no 29 February (2005 and 2006 are ordinary years).
2. Each year adds 1 odd day: total 2.
3. Friday + 2 days = Sunday.

Teacher's Note:
1. Check whether a 29 February falls between the two dates, not just whether a year is leap.
2. Same date one year later moves 1 weekday ahead (2 if a 29 February is crossed).

Answer: (d) Friday

Explanation:
1. 20 Feb 1996 to 20 Feb 1997 includes 29 Feb 1996, so it is 366 days = 2 odd days.
2. 20 Feb 1997 to 20 Feb 1998 is 365 days = 1 odd day.
3. Total 3 odd days: Tuesday + 3 = Friday.

Teacher's Note:
1. A date before 29 February in a leap year gains 2 weekdays by the next year.
2. Add odd days year by year and reduce modulo 7.

Answer: (a) Two

Explanation:
1. 'The day after the day before yesterday' = yesterday. So five days ago, yesterday was Thursday, i.e. five days ago was Friday.
2. Today = Friday + 5 = Wednesday.
3. 'Three days before the day after tomorrow' = yesterday. Sunday was yesterday on a Monday.
4. The most recent Monday before Wednesday is 2 days ago.

Teacher's Note:
1. Simplify each phrase into a single offset (for example, day after the day before yesterday = -1).
2. Fix 'today' first; every other day in the question is measured from it.

Answer: (b) September, December

Explanation:
1. Two months share a calendar when the days between their first dates form a multiple of 7.
2. September to December: 30 + 31 + 30 = 91 days = 13 weeks, 0 odd days.
3. Others: April-December 244 days (6 odd), May-August 92 (1 odd), August-December 122 (3 odd).
4. So September and December have the same calendar.

Teacher's Note:
1. Add the days of the months in between and check for 0 odd days.
2. September-December and April-July always match; January-October matches only in an ordinary year.

Answer: (d) Friday

Explanation:
1. 2000 years give 0 odd days; 2001-2008 have 2 leap years: 2 x 2 + 6 x 1 = 10 = 3 odd days.
2. 1 Jan to 28 Aug 2009: Jan 3 + Feb 0 + Mar 3 + Apr 2 + May 3 + Jun 2 + Jul 3 + 28 Aug (0) = 16 = 2 odd days.
3. Total = 0 + 3 + 2 = 5 odd days, which means Friday.

Teacher's Note:
1. Split the date into complete 400-year blocks, the remaining full years, and the days of the current year.
2. Map the final odd-day count to a weekday: 0 Sunday, 1 Monday, ..., 5 Friday, 6 Saturday.

Answer: (d) Saturday

Explanation:
1. Nine days ago was a Thursday.
2. 9 days = 1 week + 2 days.
3. Thursday + 2 days = Saturday.

Teacher's Note:
1. Reduce any day gap modulo 7 before counting.
2. Counting forward from the known day is safer than counting backward from today.

Answer: (c) Thursday

Explanation:
1. 2008 is a leap year with 366 days = 52 weeks + 2 days.
2. So 1 January 2009 is 2 weekdays after 1 January 2008.
3. Tuesday + 2 = Thursday.

Teacher's Note:
1. A leap year has 2 odd days; an ordinary year has 1.
2. A year is a leap year if divisible by 4, except century years, which must be divisible by 400.