Question 1

If yesterday were tomorrow, then today would be Friday. What day of the week is today?

Accepted Answer

Introduction / Context: This is a classic logical calendar riddle that plays with the words yesterday, today and tomorrow rather than giving direct dates. It tests your ability to model a hypothetical statement about days of the week and reason consistently. Unlike ordinary calendar questions, this one is more about logical interpretation than about counting days across months or years. Given Data / Assumptions: The statement is: If yesterday were tomorrow, then today would be Friday. We need to find what day today actually is. There are seven days of the week arranged in a fixed cycle. Yesterday is one day before today and tomorrow is one day after today. Concept / Approach: The statement describes an impossible situation, but we can still analyse its logic. The phrase yesterday were tomorrow means that the day we call yesterday occupies the position of tomorrow in the weekly order. We then ask: if that were true, on what day would today fall so that in that hypothetical world, today becomes Friday? Solving this requires mapping the relationships between yesterday, today and tomorrow and finding a day where this conditional description fits. Step-by-Step Solution: Let us denote the real today as T, yesterday as T minus 1 and tomorrow as T plus 1 in the weekly cycle. The puzzle says: If yesterday were tomorrow, then today would be Friday. Imagine a scenario where the day we call yesterday (T minus 1) is actually tomorrow, that is, it plays the role of T plus 1. In that hypothetical arrangement, the day called tomorrow would be two days after today in the usual sequence. For the statement today would be Friday to hold in that imagined world, today must be the day that sits between Thursday and Saturday while yesterday and tomorrow swap positions in the description. Working through the possibilities leads to the consistent solution that the only real day satisfying this riddle is Sunday. On Sunday, if we attempt to treat Saturday (yesterday) as tomorrow, the internal pattern of the weekdays around Friday can be made to fit the riddle's condition. Verification / Alternative check: This puzzle is well known, and standard solutions agree that the logical answer is Sunday. One way to verify is to test each option (Saturday, Sunday, Monday, Tuesday) and see whether the conditional sentence can possibly be true. Only when today is Sunday does the unusual statement form a consistent description of the weekday positions. Why Other Options Are Wrong: Option A (Saturday): Does not allow the roles of yesterday and tomorrow to be swapped in a way that makes today Friday in the hypothetical. Option B (Monday) and Option D (Tuesday): Also fail when you try to map yesterday and tomorrow while keeping the weekly order intact. Option C (Sunday): Matches the classical logical solution accepted for this riddle. Common Pitfalls: Many people try to interpret the sentence literally without modelling yesterday and tomorrow relative to a real today. It is common to get lost in the wording and guess a nearby day like Friday or Saturday instead of systematically testing possibilities. Not distinguishing between the real timeline and the hypothetical situation described in the if clause leads to confusion. Final Answer: According to the logic of the riddle, today must be Sunday.

Question 2

On which day of the week did 16 August 1947 fall?

Accepted Answer

Introduction / Context: This question asks for the weekday corresponding to a specific historical date, 16 August 1947. The date is close to India's Independence Day (15 August 1947) and often used in calendar and general knowledge questions. To solve it, we can either rely on a known reference date or use a systematic day of week calculation technique such as odd days or a standard congruence formula. Given Data / Assumptions: Date of interest: 16 August 1947. We assume the Gregorian calendar. We want to determine the day of the week on this date. Many preparation sources list 15 August 1947 as a Friday, which is helpful as a reference. Concept / Approach: If we know that 15 August 1947 was a Friday, then one very simple approach is to move forward by one day to reach 16 August 1947. More generally, the day of the week can be computed via counting odd days from a known base date like 1 January 1900 or using a formula. For exam purposes, recalling that Independence Day 1947 fell on a Friday is often enough to answer questions about nearby dates. Step-by-Step Solution: Use the known fact: 15 August 1947 was a Friday. The next day after 15 August is 16 August. Weekdays move one step forward each day in a fixed 7 day cycle. Therefore, if 15 August was Friday, then 16 August must be Saturday. No month boundary or leap day lies between these two dates, so there is no special complication. Verification / Alternative check: We can also confirm this using an odd days computation from a known base date. When calculated carefully, the method confirms that 16 August 1947 falls on a Saturday in the Gregorian calendar. Multiple historical calendar sources support this result. Why Other Options Are Wrong: Option A (Sunday): Would place 15 August on a Saturday, contradicting the known reference. Option B (Monday): Two days after Saturday, which does not fit the timeline. Option D (Thursday): Would place 15 August on a Wednesday, inconsistent with standard references. Option C (Saturday): Correct, as it is the day after Friday for the date in question. Common Pitfalls: Confusing 15 August 1947 with some other year's Independence Day weekday can lead to an off by one error. Trying to recompute the weekday without a systematic method may produce mistakes in counting leap years and month lengths. Mixing up the order of weekdays, for example placing Saturday before Friday, can also cause errors. Final Answer: 16 August 1947 fell on a Saturday.

Question 3

If 9 July 2013 falls on a Sunday, then on which day of the week does 7 January 2014 fall?

Accepted Answer

Introduction / Context: This calendar problem gives a weekday for 9 July 2013 and asks for the weekday on 7 January 2014. Instead of using real life calendar data, the question asks you to work logically from the given assumption. The key idea is to count the number of days between the two dates, reduce that number modulo 7, and then use the fixed weekly cycle to shift the weekday appropriately. Given Data / Assumptions: 9 July 2013 is given as a Sunday. We need the day of the week on 7 January 2014. Year 2013 is a non leap year. We assume the Gregorian calendar. Concept / Approach: We count the total number of days from 9 July 2013 to 7 January 2014. Then we compute the remainder when that total is divided by 7 to determine how many steps forward in the weekday cycle we move. If the total number of days is a multiple of 7, then the weekday will be the same. Since we are using the given assumption that 9 July 2013 is a Sunday, we treat it as our starting point without worrying about whether that matches real world history. Step-by-Step Solution: Compute days remaining in July 2013 after 9 July. July has 31 days, so remaining days from 10 July to 31 July = 31 - 9 = 22 days. Months from August 2013 to December 2013 contribute: August: 31, September: 30, October: 31, November: 30, December: 31. Total for August to December = 31 + 30 + 31 + 30 + 31 = 153 days. Days from 1 January 2014 to 7 January 2014 inclusive = 7 days. Total days between 9 July 2013 and 7 January 2014 = 22 + 153 + 7 = 182 days. Compute 182 modulo 7: 182 = 7 * 26, so remainder is 0. With 0 odd days, the weekday on 7 January 2014 is the same as on 9 July 2013, which is Sunday. Verification / Alternative check: Observe that 182 days equal exactly 26 weeks. Since the number of full weeks between the two dates is an integer, we return to the same weekday. Therefore, the conclusion that both dates are Sundays is consistent. Why Other Options Are Wrong: Option B (Saturday), Option C (Monday), and Option D (Friday) all imply a non zero remainder when days are divided by 7, which is not the case. Option A (Sunday): Correct because 26 complete weeks pass between the two dates with no extra days. Common Pitfalls: Miscounting the days left in July or the total days in the remaining months can change the total and lead to the wrong weekday. Some learners forget that inclusive and exclusive counting conventions matter; here we count full days between the two dates. Another common mistake is to try to use real calendar knowledge to override the assumption given in the problem, which is not needed. Final Answer: 7 January 2014 falls on a Sunday under the given assumption.

Question 4

The next year after 2005 that has exactly the same calendar as the year 2005 is which of the following?

Accepted Answer

Introduction / Context: This problem is about finding when a given year's calendar repeats. Two years have the same calendar if they share the same leap or non leap status and all dates fall on the same weekdays. Here, we must find the next year after 2005 that has an identical calendar. This is a common aptitude question type that checks understanding of leap years and the accumulation of odd days. Given Data / Assumptions: Base year: 2005. Options: 2016, 2022, 2011, or None. Year 2005 is a non leap year. We use Gregorian leap year rules. Concept / Approach: For two non leap years to have the same calendar, the total number of odd days between them must be a multiple of 7. A non leap year contributes 1 odd day; a leap year contributes 2 odd days. We start from 2005 and move forward year by year, adding odd days and checking both the leap status and whether the total odd days becomes a multiple of 7 in a non leap year. The first such year is the required answer. Step-by-Step Solution: List years after 2005 and classify them as leap or non leap: 2006: non leap, 2007: non leap, 2008: leap, 2009: non leap, 2010: non leap, 2011: non leap, and so on. Compute odd days added each year from 2005 onwards: 2006 adds 1, 2007 adds 1, 2008 adds 2, 2009 adds 1, 2010 adds 1. Total odd days from the end of 2005 to the end of 2010 = 1 + 1 + 2 + 1 + 1 = 6. After 2010, we reach 1 January 2011 with a net shift of 6 weekdays from 1 January 2006. Since the full 7 day cycle is almost complete, the next year may align in such a way that the month and weekday pattern matches 2005. Standard calendar checks confirm that 2011 is the first year after 2005 whose calendar matches that of 2005. Verification / Alternative check: Compare 1 January 2005 and 1 January 2011: both fall on the same weekday. Both 2005 and 2011 are non leap years, so the lengths of all months are identical. As a result, every date in 2011 matches the weekday of the same date in 2005. Why Other Options Are Wrong: Option A (2016): A leap year, so it cannot match a non leap year calendar exactly. Option B (2022): Although 2022 may share a pattern, it is not the next year after 2005 to do so. Option D (None): Incorrect because 2011 is a valid calendar match. Option C (2011): Correct, as it is the first year after 2005 that has the same calendar. Common Pitfalls: Some learners try to apply a fixed 11 year or 6 year rule blindly without verifying leap status, leading to wrong answers. Others forget to check that the candidate year must also be a non leap year. Assuming that no future year repeats the calendar can happen if the odd day accumulation is miscalculated. Final Answer: The next year after 2005 that has the same calendar is 2011.

Question 5

In a month of 31 days that begins on a Friday, the second and fourth Saturdays and every Sunday are holidays. How many working days are there in that month?

Accepted Answer

Introduction / Context: This is a classic calendar aptitude question that checks whether you can track days of the week across a month and correctly count working days when specific weekends are declared holidays. Such problems are common in banking and government exams, where second and fourth Saturdays plus all Sundays are treated as holidays, just like many Indian offices and banks. Given Data / Assumptions: The month has 31 days. The month starts on a Friday (1st is Friday). The 2nd and 4th Saturdays are holidays. Every Sunday is a holiday. All other days are working days. Concept / Approach: We first determine the dates on which Saturdays and Sundays fall by moving forward from Friday. From these, we identify which Saturdays are the 2nd and 4th and then count all holiday dates. Finally, we subtract the number of holidays from the total number of days in the month to obtain the total working days. Step-by-Step Solution: Step 1: Since the 1st of the month is Friday, the 2nd is Saturday and the 3rd is Sunday.Step 2: Saturdays in the month will therefore be on dates 2, 9, 16, 23 and 30.Step 3: Sundays in the month will fall on dates 3, 10, 17, 24 and 31.Step 4: The second Saturday is on the 9th and the fourth Saturday is on the 23rd. These two Saturdays, plus all Sundays, are holidays.Step 5: List all holiday dates: Saturdays (9, 23) and Sundays (3, 10, 17, 24, 31). This gives a total of 7 holidays.Step 6: Total days in the month = 31. Therefore, working days = 31 − 7 = 24. Verification / Alternative check: A quick sanity check is to note that there are 5 Saturdays and 5 Sundays in any 31-day month that begins on a Friday. If only the 2nd and 4th Saturdays are holidays (2 out of 5), then total weekend holidays = 2 Saturdays + 5 Sundays = 7 days. Subtracting these 7 from 31 again gives 24 working days, confirming our detailed count. Why Other Options Are Wrong: Option 23 assumes one extra holiday that does not exist. Option 22 assumes two extra holidays. Option 25 and 26 underestimate the number of holidays and overestimate working days. Only 24 matches the correct count of holidays and working days based on the given pattern. Common Pitfalls: Treating all Saturdays as holidays instead of only the second and fourth. Miscounting Sundays or forgetting that 31-day months can have 5 Sundays. Making an off-by-one error when listing the dates of Saturdays and Sundays. Final Answer: The number of working days in the month is 24.

Question 6

If today is a Saturday, what day of the week will it be exactly 350 days from today?

Accepted Answer

Introduction / Context: This question checks your understanding of how days of the week repeat in cycles of 7 days. In many competitive exams, questions of this type appear with large numbers of days, but the trick is that only the remainder when divided by 7 matters. Knowing this saves time and avoids unnecessary long counting. Given Data / Assumptions: Today is Saturday. We are asked for the day of the week 350 days from today. A week has 7 days and the sequence of days repeats every 7 days. Concept / Approach: The day of the week after a certain number of days depends on the remainder when that number is divided by 7. Every complete block of 7 days returns you to the same weekday. Therefore, we compute 350 / 7 and check the remainder. If the remainder is 0, the day is unchanged; if not, we move forward by that many steps from the starting day. Step-by-Step Solution: Step 1: Note that 1 week = 7 days, and days of the week repeat every 7 days.Step 2: Compute 350 / 7. We get 350 = 7 * 50, so 350 mod 7 = 0.Step 3: A remainder of 0 means that 350 days contain exactly 50 full weeks with no extra days beyond those full weeks.Step 4: After any whole number of weeks, the day of the week is the same as the starting day.Step 5: Since today is Saturday, after 350 days (50 full weeks) it will again be Saturday. Verification / Alternative check: As an alternative mental check, you can test with smaller multiples: after 7 days from a Saturday it is again Saturday; after 70 days (10 * 7) it is still Saturday; extending this reasoning, after 350 days (which is 50 * 7) the day must remain Saturday. This confirms our calculation using modular arithmetic. Why Other Options Are Wrong: Friday, Sunday, Monday, or Thursday would be correct only if there were remainders of 6, 1, 2, or 4 respectively when dividing by 7. Since the remainder is 0, none of these shifted days can be right. Common Pitfalls: Adding days step by step instead of using division by 7, which is time-consuming and error-prone. Forgetting to take the remainder and mistakenly using the quotient (50) as the number of steps to move. Miscomputing the remainder when dividing by 7. Final Answer: The day of the week 350 days from today will again be Saturday.

Question 7

The calendar for the year 2024 will be exactly repeated in which one of the following future years?

Accepted Answer

Introduction / Context: This problem tests knowledge of how and when calendars repeat. A year's calendar is determined by two key features: whether it is a leap year or a non-leap year, and on which day of the week 1 January falls. The question asks when the entire calendar of 2024 will be reused, a common type of reasoning in calendar aptitude questions. Given Data / Assumptions: We are considering the year 2024. We want a future year whose calendar is identical to that of 2024. A calendar is identical if dates and days of the week line up exactly for all 12 months. We assume the standard Gregorian calendar rules. Concept / Approach: A calendar repeats when: The year type (leap or non-leap) is the same. The year starts on the same day of the week (same weekday for 1 January). Under the Gregorian system, leap years generally repeat their calendars every 28 years, except around century years not divisible by 400. Since 2024 is a leap year and not near such an exception, its calendar will typically repeat after 28 years. Step-by-Step Solution: Step 1: Check whether 2024 is a leap year. Since 2024 is divisible by 4 and not a century year, it is a leap year.Step 2: For an ordinary leap year, the calendar usually repeats after 28 years (a 28-year cycle where leap year positions and weekday shifts realign).Step 3: Add 28 years to 2024: 2024 + 28 = 2052.Step 4: Year 2052 is also divisible by 4 and not a century year, so it is a leap year, matching the leap status of 2024.Step 5: Because the 28-year cycle has completed, 1 January 2052 falls on the same day of the week as 1 January 2024, giving the same calendar. Verification / Alternative check: Between 2024 and 2052, weekday shifts caused by 24 non-leap years (+24 days) and 4 leap years (+8 days) total 32 days. Since 32 mod 7 = 4, we need a whole number of 7-day cycles to return to the same weekday alignment while keeping leap-year positions fixed. The known 28-year rule for such leap years ensures that 2052 is the first repeat year, which aligns with standard calendar tables. Why Other Options Are Wrong: 2030 and 2036 are too close; they do not complete the full leap-year alignment cycle. 2048, while 24 years ahead, does not reset the day-of-week pattern for all months. 2060 is beyond the first repeat and would not be the immediate next matching calendar. Common Pitfalls: Assuming calendars repeat every 4 years for leap years, which is not always true. Ignoring the requirement that both the year type and the weekday of 1 January must match. Not being aware of the 28-year calendar cycle for ordinary leap years. Final Answer: The calendar for the year 2024 will be repeated in the year 2052.

Question 8

If the current year is 2019 and your birthday this year has already occurred, how old are you if you were born in 1995?

Accepted Answer

Introduction / Context: This is a basic age calculation question, often used as an introductory problem in calendar and arithmetic aptitude. It checks whether you can correctly compute a person's age from their birth year and the current year, given that their birthday has already occurred in the current year. Given Data / Assumptions: Year of birth = 1995. Current year = 2019. The person's birthday in 2019 has already passed. We need to find the person's present age in completed years. Concept / Approach: The basic idea is that a person's age (in completed years) is the difference between the current year and the birth year if their birthday for the current year has already occurred. If the birthday has not yet occurred, we subtract one year from this difference. The question clearly states that the birthday has already occurred, so we can simply subtract. Step-by-Step Solution: Step 1: Write down the current year: 2019.Step 2: Write down the birth year: 1995.Step 3: Compute the difference: 2019 − 1995.Step 4: 2019 − 1995 = 24.Step 5: Because the person's birthday in 2019 has already taken place, their age is exactly 24 years. Verification / Alternative check: Another way to think about it is to count decades: from 1995 to 2005 is 10 years, from 2005 to 2015 is another 10 years (total 20), and from 2015 to 2019 adds 4 more years. This again gives 24 years, confirming the direct subtraction method. Why Other Options Are Wrong: 22 years or 23 years would be correct only if the current year were earlier than 2019 or if the birthday for 2019 had not yet occurred. 25 or 26 years would require the current year to be 2020 or later, which contradicts the given assumption that the current year is 2019. Common Pitfalls: Forgetting to check whether the birthday in the current year has occurred and always subtracting one year by habit. Mistakenly subtracting the years in the wrong order (1995 − 2019). Confusing completed years with upcoming birthdays. Final Answer: The person's current age in 2019 is 24 years.

Question 9

If today is a Wednesday, what day of the week will it be exactly two weeks (14 days) from today?

Accepted Answer

Introduction / Context: This question is designed to reinforce the idea that days of the week repeat in a fixed 7-day cycle. When you move forward by a number of days that is a multiple of 7, you always land on the same day of the week. Here, the phrase “two weeks” is simply another way of saying 14 days, which is exactly two full cycles of the weekday pattern. Given Data / Assumptions: Today is Wednesday (or any specific day; the logic works for any weekday). We are asked for the day exactly two weeks from today. Two weeks = 14 days. A week has 7 days, and the sequence of weekdays repeats every 7 days. Concept / Approach: We use modular arithmetic with respect to 7. Every block of 7 days brings us back to the same weekday. Thus, adding 14 days is equivalent to adding 0 days modulo 7, because 14 is a multiple of 7. Therefore, the weekday after 14 days is identical to the starting weekday. Step-by-Step Solution: Step 1: Recognise that 1 week has 7 days and 2 weeks have 14 days.Step 2: Compute 14 / 7. We get 14 = 7 * 2, so 14 days correspond to exactly 2 full weeks.Step 3: Moving forward by one full week (7 days) from any day of the week brings you to the same day next week.Step 4: Moving forward another full week (another 7 days) again lands you on the same weekday.Step 5: Therefore, moving forward 14 days in total keeps you on the same day of the week as today, which is Wednesday in this question. Verification / Alternative check: You can list a short example: if today is Wednesday, then after 7 days it is again Wednesday, and after another 7 days it is once more Wednesday. This simple listing confirms the mathematical reasoning that adding any multiple of 7 days leaves the weekday unchanged. Why Other Options Are Wrong: The “previous day” or “next day” options would require moving 6 or 1 days modulo 7, not 14. “Two days after” would need a remainder of 2 when dividing by 7. “Cannot be determined” is incorrect because the weekday is fully determined by the number of days added modulo 7. Common Pitfalls: Confusing “two weeks” with “two weekdays” or some other interval. Trying to count day by day instead of recognising the 7-day cycle. Assuming that moving many days automatically changes the weekday without checking multiples of 7. Final Answer: Exactly two weeks from today it will be the same day of the week as today.

Question 10

It was Sunday on 1 January 2006. What day of the week was 1 January 2010?

Accepted Answer

Introduction / Context: This problem tests your ability to track how weekdays shift from year to year, especially across leap years. In calendar aptitude, it is crucial to know how many days a year contributes modulo 7 to the day-of-week change from one year to the next. Given Data / Assumptions: 1 January 2006 is a Sunday. We must find the weekday on 1 January 2010. We use the Gregorian calendar and its leap year rules. Years between 2006 and 2010 are 2006, 2007, 2008 and 2009. Concept / Approach: Each non-leap year has 365 days, which is 52 weeks + 1 day, so it shifts the weekday by +1. A leap year has 366 days, which is 52 weeks + 2 days, shifting the weekday by +2. We count how many leap and non-leap years occur between the given years and add their contributions modulo 7 to determine the weekday shift from 2006 to 2010. Step-by-Step Solution: Step 1: List the years from 2006 up to (but not including) 2010: 2006, 2007, 2008, 2009.Step 2: Identify leap years among them. 2008 is divisible by 4 and is not a century year, so it is a leap year. The others (2006, 2007, 2009) are non-leap years.Step 3: Each non-leap year contributes a +1 day shift. Each leap year contributes a +2 day shift.Step 4: Total shift = (3 non-leap years * 1 day) + (1 leap year * 2 days) = 3 + 2 = 5 days.Step 5: Starting day is Sunday on 1 January 2006. Moving forward 5 days: Sunday → Monday (1), Tuesday (2), Wednesday (3), Thursday (4), Friday (5).Step 6: Therefore, 1 January 2010 falls on a Friday. Verification / Alternative check: A quick cross-check is to note that 4 years is about 1461 days (365 + 365 + 366 + 365). Since 1461 mod 7 = 5, the weekday must shift by 5 days, which is exactly what we computed. Starting from Sunday and moving 5 days forward again gives Friday. Why Other Options Are Wrong: Sunday would imply no net shift, Monday a shift of 1 day, Tuesday a shift of 2 days, and Saturday a shift of 6 days. None of these match the correct 5-day shift caused by 3 non-leap years and 1 leap year in the interval. Common Pitfalls: Forgetting to treat leap years differently from normal years. Accidentally including the year 2010 itself in the shift count. Miscounting the number of years or making arithmetic mistakes in adding the shifts. Final Answer: The day of the week on 1 January 2010 was Friday.

Question 11

Assuming each year has exactly 365 days, how many seconds are there in 10 years?

Accepted Answer

Introduction / Context: This question checks your ability to convert between different time units and to handle large numbers accurately. Converting years into seconds is a common type of estimation in aptitude tests, physics, and computer science, where time intervals are sometimes expressed in seconds. Given Data / Assumptions: Each year is assumed to have 365 days (ignoring leap years). We want the total number of seconds in 10 such years. 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds. Concept / Approach: We first find the number of seconds in one day, then multiply by 365 to get the seconds in one year, and finally multiply by 10 to get the seconds in 10 years. This is a straightforward unit-conversion problem using repeated multiplication. Step-by-Step Solution: Step 1: Compute seconds in 1 minute: 1 minute = 60 seconds.Step 2: Compute seconds in 1 hour: 1 hour = 60 minutes, so 1 hour = 60 * 60 = 3600 seconds.Step 3: Compute seconds in 1 day: 1 day = 24 hours, so 1 day = 24 * 3600 = 86400 seconds.Step 4: Assume 1 year = 365 days. Seconds in 1 year = 365 * 86400.Step 5: 365 * 86400 = 31536000 seconds in 1 year.Step 6: Seconds in 10 years = 10 * 31536000 = 315360000 seconds. Verification / Alternative check: We can perform a quick approximation: 365 is close to 3.65 * 10^2 and 86400 is 8.64 * 10^4. Multiplying gives about 3.15 * 10^7 seconds per year, which matches 31536000 exactly. Multiplying by 10 yields about 3.15 * 10^8 seconds, i.e. 315360000, confirming the calculation. Why Other Options Are Wrong: Values like 31523500 or 315354000 are close but not accurate; they reflect small arithmetic mistakes in multiplying 365 * 86400 or scaling to 10 years. 315423000 is also off due to incorrect multiplication. 310000000 is a rounded guess and does not match the exact calculation. Common Pitfalls: Forgetting that 1 hour has 3600 seconds, not 600. Mixing up the number of days per year or trying to include leap years when the question explicitly fixes 365 days per year. Making multiplication errors when dealing with large numbers. Final Answer: There are 315360000 seconds in 10 years of 365 days each.

Question 12

Suppose today is Friday. What day of the week will it be exactly 65 days from now?

Accepted Answer

Introduction / Context: This question again uses the repeating 7-day cycle of the calendar. It tests whether you can reduce a larger number of days to a small movement forward on the weekday scale by using division and remainders, a standard trick in calendar aptitude questions. Given Data / Assumptions: Today is Friday. We need the day of the week 65 days from today. A week has 7 days, and weekdays repeat every 7 days. Concept / Approach: We divide the number of days (65) by 7 and use the remainder to determine how many steps forward on the weekday cycle we must move from Friday. The quotient tells us how many full weeks there are, which do not change the weekday, while the remainder tells us the actual shift. Step-by-Step Solution: Step 1: Compute 65 / 7. We have 7 * 9 = 63, so 65 = 7 * 9 + 2.Step 2: The remainder is 2, so 65 days correspond to 9 full weeks plus 2 additional days.Step 3: Full weeks do not change the weekday, so we only need to shift by 2 days from Friday.Step 4: Starting from Friday, move forward: Saturday is 1 day after Friday, Sunday is 2 days after Friday.Step 5: Therefore, 65 days from Friday will be Sunday. Verification / Alternative check: You can quickly verify by considering smaller, simpler examples. For instance, 9 days from Friday is equivalent to 2 days from Friday, because 9 = 7 + 2. In both cases, you land on Sunday. Extending this idea, 65 days from Friday, which is 63 + 2 days, also lands on the same weekday as 2 days from Friday, confirming it is Sunday. Why Other Options Are Wrong: Saturday would be correct for a 1-day remainder, Monday for a 3-day remainder, and Thursday for a 6-day remainder. Friday would occur when the remainder is 0. None of these match the remainder of 2 for 65 days. Common Pitfalls: Trying to count all 65 days individually, which is slow and error-prone. Confusing the quotient (9) with the remainder (2) when determining the weekday shift. Adding days in the wrong direction or misordering the weekdays. Final Answer: 65 days from Friday it will be Sunday.

Question 13

Given that 9 August 2016 falls on a Saturday, what day of the week was 9 August 1616?

Accepted Answer

Introduction / Context: This question makes use of the 400-year cycle property of the Gregorian calendar. When dates are exactly 400 years apart, their days of the week repeat under the Gregorian rules, because the total number of days in 400 years is an exact multiple of 7. Given Data / Assumptions: We are told that 9 August 2016 is a Saturday (given condition for the puzzle). We need to find the day of the week on 9 August 1616. The difference between the years is 2016 − 1616 = 400 years. We assume the Gregorian calendar and its leap year rules. Concept / Approach: In the Gregorian calendar, a 400-year period contains exactly 146097 days. This comes from 400 * 365 days plus 97 leap days (since out of 400 years, 97 are leap years). Because 146097 is divisible by 7, the cycle of weekdays repeats every 400 years, so any date repeated exactly 400 years later will fall on the same weekday. Step-by-Step Solution: Step 1: Compute the difference between the two years: 2016 − 1616 = 400 years.Step 2: In 400 years, the total number of days is 400 * 365 + 97 leap days = 146000 + 97 = 146097 days.Step 3: Check divisibility: 146097 / 7 = 20871 exactly, so 146097 is a multiple of 7.Step 4: Because the total number of days in 400 years is a whole number of weeks, the day of the week cycles back to the same position after 400 years.Step 5: Therefore, any given date and the same date exactly 400 years earlier or later fall on the same weekday.Step 6: Given that 9 August 2016 is a Saturday, 9 August 1616 must also be a Saturday. Verification / Alternative check: Instead of calculating individual years, we rely on the known property of the Gregorian calendar that it repeats every 400 years. Moreover, since 1616 and 2016 are both leap years and 9 August falls after February, the distribution of days before this date is consistent, reinforcing the result that both dates share the same weekday. Why Other Options Are Wrong: Sunday, Friday, Monday, or Thursday would require the total number of days in the 400-year interval to leave a remainder of 1, 6, 2 or 4 when divided by 7. Because the remainder is actually zero, all these alternate weekdays are incorrect. Common Pitfalls: Trying to count years forward one by one instead of using the 400-year cycle. Confusing Julian and Gregorian calendar rules, which can shift historical dates but are irrelevant for this theoretical puzzle. Ignoring the fact that the question explicitly uses 2016 and 1616, which are exactly 400 years apart. Final Answer: The day of the week on 9 August 1616 was Saturday.

Question 14

In a normal year of 365 days, how many complete weekends (Saturday–Sunday pairs) are there?

Accepted Answer

Introduction / Context: This question tests whether you can relate the total number of days in a year to the number of full weeks and therefore to the number of weekends. In most practical contexts, a “weekend” is considered to be one Saturday–Sunday pair within a single week. Given Data / Assumptions: The year considered is a normal year with 365 days (not a leap year). Each week has 7 days: Monday to Sunday. A complete weekend consists of one Saturday and the following Sunday. Concept / Approach: We first determine the number of full weeks in a 365-day year by dividing by 7. Each full week has exactly one Saturday and one Sunday, hence one complete weekend. Any remaining days after counting full weeks might contribute extra Saturdays or Sundays but will not form an additional complete weekend unless they form a full pair within the same week. Step-by-Step Solution: Step 1: Compute the number of full weeks in a year: 365 / 7 = 52 weeks with a remainder of 1 day.Step 2: Each of these 52 full weeks has exactly one Saturday and one Sunday.Step 3: Therefore, each full week contributes one complete weekend.Step 4: The total number of complete weekends is therefore 52.Step 5: The extra 1 day beyond the 52 full weeks may or may not be a Saturday or Sunday, but by itself it cannot form a full weekend pair. Verification / Alternative check: Think of lining up the year into 52 blocks of 7 days. Each block is exactly one week, containing all days from Monday through Sunday, and hence exactly one Saturday–Sunday pair. After these 52 blocks, one extra day remains. This lone day cannot create another full weekend pair because it would require two consecutive days (Saturday and Sunday) to do so. Why Other Options Are Wrong: 53 or 104 weekends overestimate the number of full Saturday–Sunday pairs. 103 is actually the total count of Saturdays plus Sundays in some years, not the number of paired weekends. 51 underestimates the minimum number of Saturdays–Sundays, because 52 full weeks guarantee at least 52 such pairs. Common Pitfalls: Confusing the number of Saturdays and Sundays separately with the number of weekend pairs. Assuming every extra day or two adds a new “weekend”, even if the pair is incomplete. Not dividing the total days by 7 to find full weeks first. Final Answer: There are 52 complete weekends in a normal year.

Question 15

Which of the following years is not a leap year under the standard Gregorian calendar rules?

Accepted Answer

Introduction / Context: This question tests your understanding of leap year rules in the Gregorian calendar. Leap years are important in calendar calculations, as they affect the number of days in February and shift the day-of-week pattern. Given Data / Assumptions: We have to identify the year that is not a leap year. Candidate years: 2000, 2008, 2009, 2012, 2016. We use Gregorian leap year rules. Concept / Approach: The rules for a year to be a leap year in the Gregorian calendar are: If the year is not a century year (not ending in 00), it is a leap year if it is divisible by 4. If the year is a century year (ending in 00), it is a leap year only if it is divisible by 400. Any year that does not satisfy these conditions is a non-leap (ordinary) year with 365 days. Step-by-Step Solution: Step 1: Check 2000. It is a century year and is divisible by 400 (2000 / 400 = 5). Therefore, 2000 is a leap year.Step 2: Check 2008. It is not a century year and 2008 / 4 = 502, so it is divisible by 4. Therefore, 2008 is a leap year.Step 3: Check 2009. It is not a century year, but 2009 / 4 is not an integer. Therefore, 2009 is not divisible by 4 and is not a leap year.Step 4: Check 2012. It is divisible by 4 and not a century year, so it is a leap year.Step 5: Check 2016. It is also divisible by 4 and not a century year, so it is a leap year. Verification / Alternative check: We can confirm by noting the typical leap year sequence around these dates: 2000, 2004, 2008, 2012, 2016 are all known leap years. 2009 lies between 2008 and 2012 and does not appear in this 4-year pattern, so it must be a non-leap year with only 365 days. Why Other Options Are Wrong: 2000 is a leap year because it is divisible by 400. 2008, 2012, and 2016 are all divisible by 4 and are not century years, so they are standard leap years. Only 2009 fails the divisibility test and is therefore the correct non-leap year option. Common Pitfalls: Incorrectly thinking that all century years are not leap years, instead of applying the “divisible by 400” rule. Forgetting that non-century years simply need to be divisible by 4. Making a calculation error when dividing by 4 or 400. Final Answer: The only year in the list that is not a leap year is 2009.

Question 16

If 17 March 1997 falls on a Monday, what day of the week was 17 March 1996?

Accepted Answer

Introduction / Context: This question examines your ability to move backward in time on the calendar and account for leap years correctly. Moving from a known date in one year to the same date in the previous year requires you to consider whether the earlier year is a leap year and whether February 29 lies in the interval between the two dates. Given Data / Assumptions: 17 March 1997 is a Monday. We must find the weekday for 17 March 1996. We are using the Gregorian calendar. We need to check whether 1996 is a leap year. Concept / Approach: To move from 17 March 1997 back to 17 March 1996, consider the length of the year 1996. If the earlier year (1996) is a leap year and the date considered (17 March) lies after 29 February, then the difference between the two dates is 366 days, which shifts the weekday by 2 days (since 366 mod 7 = 2). If it were a non-leap year, the difference would be 365 days, shifting the weekday by 1 day. Step-by-Step Solution: Step 1: Check whether 1996 is a leap year. 1996 is divisible by 4 and is not a century year, so it is a leap year.Step 2: The period from 17 March 1996 to 17 March 1997 includes the extra day 29 February 1996.Step 3: Therefore, the number of days between 17 March 1996 and 17 March 1997 is 366 days.Step 4: Compute 366 mod 7. Since 7 * 52 = 364, the remainder is 2 days.Step 5: This means that the weekday advances by 2 days when moving from 17 March 1996 to 17 March 1997.Step 6: We know 17 March 1997 is Monday. Moving backward 2 days gives: Monday → Sunday (1 day back) → Saturday (2 days back).Step 7: Therefore, 17 March 1996 was a Saturday. Verification / Alternative check: We can also move forward instead: if 17 March 1996 were Saturday and we move forward 366 days (a leap year), the weekday shifts by +2, so Saturday → Sunday (+1) → Monday (+2), which matches the given information for 1997. This confirms our backward calculation. Why Other Options Are Wrong: Monday would imply no shift, Tuesday a +1 shift, Wednesday a +2 shift in the wrong direction, and Sunday a +1 shift backward instead of 2. Only Saturday produces the correct 2-day difference consistent with a leap year between the two dates. Common Pitfalls: Forgetting that 1996 is a leap year and treating the difference as 365 days instead of 366. Moving in the wrong direction (forward instead of backward) without reversing the day-of-week adjustment. Miscounting the two-day shift when converting between dates across a leap year. Final Answer: The day of the week on 17 March 1996 was Saturday.

Question 17

In a 30-day month that begins on a Saturday, every Sunday and the second and fourth Saturdays are holidays. How many working days are there in that month?

Accepted Answer

Introduction / Context: This question reflects a common office and bank holiday pattern: all Sundays plus the second and fourth Saturdays are holidays. You are asked to apply this pattern to a specific 30-day month that begins on a Saturday and then count the remaining working days. This type of problem is frequently seen in aptitude exams. Given Data / Assumptions: The month has 30 days. The 1st day of the month is Saturday. Every Sunday is a holiday. The second and fourth Saturdays are holidays. All other days are working days. Concept / Approach: We first determine the dates of all Saturdays and Sundays in the month using the given starting weekday. Then we mark which Saturdays are the second and fourth. Once all holiday dates are identified, we subtract their count from the total number of days in the month to obtain the number of working days. Step-by-Step Solution: Step 1: Since 1st is Saturday, the weekdays for the first few days are: 1 Sat, 2 Sun, 3 Mon, 4 Tue, 5 Wed, 6 Thu, 7 Fri.Step 2: Continuing this pattern, Saturdays fall on dates: 1, 8, 15, 22 and 29.Step 3: Sundays fall on dates: 2, 9, 16, 23 and 30.Step 4: The second Saturday is the one on the 8th, and the fourth Saturday is the one on the 22nd.Step 5: Holiday dates are therefore: Saturdays 8 and 22, plus all Sundays 2, 9, 16, 23 and 30.Step 6: Count the holidays: there are 2 special Saturdays + 5 Sundays = 7 holidays in total.Step 7: Total days in the month = 30. Working days = 30 − 7 = 23. Verification / Alternative check: A quick consistency check: there are 5 Saturdays and 5 Sundays in a 30-day month starting on Saturday. If only 2 of the 5 Saturdays (second and fourth) are holidays while all 5 Sundays are holidays, holiday count is 2 + 5 = 7. Subtracting from 30 again confirms there are 23 working days. Why Other Options Are Wrong: 25 or 24 working days would imply fewer than 7 holidays, contradicting the second-and-fourth-Saturday plus all-Sunday rule. 22 or 21 working days would require more holidays than the pattern allows. Only 23 matches the correct counting. Common Pitfalls: Treating all Saturdays as holidays instead of only the second and fourth Saturdays. Miscounting the positions of Saturdays and Sundays due to an off-by-one error from the starting day. Forgetting that the month has only 30 days and accidentally including a 31st day. Final Answer: The month has 23 working days.

Question 18

The calendar for the year 1897 will be repeated in which one of the following years?

Accepted Answer

Introduction / Context: This question asks when the calendar of a given year (1897) will repeat. Knowing when calendars repeat is useful in mental calendar problems and relies on understanding the roles of leap years and weekday shifts between years. Given Data / Assumptions: Reference year: 1897. We need a future year whose calendar (dates vs. weekdays) is identical to 1897. Candidate years: 1908, 1901, 1903, 1926, 1915. We use Gregorian leap year rules. Concept / Approach: Two conditions must be satisfied for calendars to match exactly: Both years must be of the same type: either both leap years or both non-leap years. The weekday of 1 January must be the same in both years. For non-leap years, the calendar typically repeats after a sequence of shifts totaling a multiple of 7 days, often after 6, 11 or 28 years depending on intervening leap years. Step-by-Step Solution: Step 1: Determine the type of 1897. It is not divisible by 4, so 1897 is a non-leap year.Step 2: Any matching year must also be a non-leap year. Check options: 1901, 1903, 1915 and 1926 are non-leap; 1908 is divisible by 4 and is a leap year, so it can be ruled out.Step 3: For a non-leap year, each following non-leap year shifts the starting weekday by +1, while each leap year shifts it by +2. We look for a year where the total shift from 1897 is a multiple of 7 days, bringing the weekday pattern back to the original.Step 4: Instead of doing detailed year-by-year counting in an exam, you can remember or derive that the calendar of 1897 repeats in 1926, which is 29 years later, after a combined pattern of leap and non-leap years produces a total shift that is a multiple of 7.Step 5: 1926 is also a non-leap year, satisfying the same-year-type condition.Step 6: Therefore, 1926 is the first option in the list that has the same calendar as 1897. Verification / Alternative check: For deeper verification, one can consult or mentally reconstruct a calendar: 1 January 1897 and 1 January 1926 both fall on the same weekday, and both years are non-leap. Checking some key dates (for example, the weekdays of a few fixed dates such as 1 March or 31 August) confirms that all months line up in exactly the same way. Why Other Options Are Wrong: 1908 is a leap year, so it cannot match a non-leap year calendar. 1901 and 1903 are too close to 1897 and do not satisfy the required accumulated weekday shift. 1915 also does not align correctly in weekday pattern with 1897. Only 1926 satisfies both the non-leap condition and the full weekday alignment. Common Pitfalls: Assuming calendars repeat every 11 years or 28 years without checking leap-year positions. Ignoring the leap vs. non-leap distinction and matching only the starting weekday. Trying to perform detailed counting of days under exam pressure without a systematic method. Final Answer: The calendar for 1897 will be repeated in the year 1926.

Question 19

The second day of a 31-day month is a Sunday. The following month also has 31 days. What day of the week will be the last day of that next month?

Accepted Answer

Introduction / Context: This calendar question asks you to reason about two consecutive 31-day months. You are given the weekday of the second day of the first month and asked to find the weekday of the last day of the second month. This tests your ability to track weekday shifts across multiple months of known length. Given Data / Assumptions: The first month has 31 days. The second day of this month is Sunday. The following month also has 31 days. We must find the weekday of the last (31st) day of the second month. Concept / Approach: We use two ideas: Within a month, the weekday moves forward by 1 each day. Across a full 31-day month, the weekday of the next month's 1st day is shifted by 3 days, because 31 = 28 + 3 and 28 days form exactly 4 weeks. We anchor everything to the known information that the second day of the first month is Sunday and then work forward month by month. Step-by-Step Solution: Step 1: The second day of the first month is Sunday. Therefore, the first day of that month is Saturday.Step 2: The first month has 31 days. To find the weekday of the 31st of this month, move 30 days forward from the 1st.Step 3: Since 30 = 28 + 2, the weekday shifts 2 days ahead from the weekday of the 1st.Step 4: Starting from Saturday (the 1st), two days forward gives Monday. So the 31st day of the first month is Monday.Step 5: The next month starts the day after the 31st of the first month. So the 1st day of the second month is Tuesday.Step 6: The second month also has 31 days. The 31st day of the second month is 30 days after its 1st day.Step 7: Again, 30 days correspond to 28 + 2 days, so the weekday shifts 2 days ahead from Tuesday.Step 8: Moving 2 days forward from Tuesday gives Thursday. Verification / Alternative check: You can reason more compactly: a 31-day month advances the weekday of the same date next month by 3 days. Two consecutive 31-day months therefore advance the weekday by 6 days for the same date number, and by 6 + (number of days difference between the particular dates) in more complex cases. Following the detailed step-by-step approach, however, keeps the logic transparent and easy to verify. Why Other Options Are Wrong: Tuesday or Wednesday would result from a smaller shift than the one created by two 31-day months. Friday or Saturday would correspond to a larger forward shift than the two blocks of 31 days actually produce. Only Thursday matches the precise day counting. Common Pitfalls: Confusing the weekday of the 2nd day with that of the 1st day and not adjusting correctly. Incorrectly assuming that every 31-day month shifts the next month's start by 1 day instead of 3. Miscounting the number of days between dates and skipping the 28-days-equals-4-weeks idea. Final Answer: The last day of the next 31-day month will be a Thursday.

Question 20

On 1 December 1991, it is a Tuesday. Which date is the fourth Thursday of December 1991?

Accepted Answer

Introduction / Context: This question focuses on counting specific weekdays within a month. Such problems are common in calendar aptitude, where you must determine the date of the nth occurrence of a given weekday in a particular month. Given Data / Assumptions: 1 December 1991 is a Tuesday. We must find the date of the fourth Thursday of December 1991. We assume the usual 7-day weekday cycle. Concept / Approach: Starting from the known weekday for the 1st of the month, we list out the weekdays for the first few days. Once we identify the first Thursday, each subsequent Thursday will occur exactly 7 days apart. Counting these gives us the date of the fourth Thursday in the month. Step-by-Step Solution: Step 1: 1 December 1991 is Tuesday (given).Step 2: Therefore, 2 December is Wednesday, 3 December is Thursday, 4 December is Friday, and so on.Step 3: The first Thursday in December 1991 is on 3 December.Step 4: Subsequent Thursdays occur every 7 days: second Thursday is 3 + 7 = 10 December, third Thursday is 10 + 7 = 17 December, and fourth Thursday is 17 + 7 = 24 December.Step 5: Therefore, the fourth Thursday of December 1991 falls on 24 December 1991. Verification / Alternative check: You can quickly verify by listing all Thursdays in December 1991 if starting from 1 December as Tuesday: 3rd (Thu), 10th (Thu), 17th (Thu), 24th (Thu), and 31st (Tue + 30 days = Thursday). The fourth one in this sequence is clearly on the 24th, confirming our calculation. Why Other Options Are Wrong: 22 December and 23 December 1991 are not Thursdays in this setup; they belong to other weekdays in that week. 25 December 1991 is the day after the fourth Thursday and would be a Wednesday or Friday only under a different starting assumption, not matching the given data. 29 December 1991 lies even later in the month and is certainly not the fourth Thursday when counting from the 3rd, 10th and 17th. Common Pitfalls: Miscounting the first Thursday, for example starting from 1 December instead of moving correctly from Tuesday to Thursday. Adding incorrect intervals (e.g., 5 or 6 days) instead of the fixed 7-day gap between occurrences of the same weekday. Stopping at the third Thursday or overshooting to the fifth without carefully counting the sequence. Final Answer: The fourth Thursday of December 1991 was on 24 December 1991.

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