Clocks and Calendars for Punjab Police SI

Answer: 3 — Monday

Count the days elapsed from 1 January and reduce modulo 7. 2004 is a leap year (divisible by 4 and not a century), so February has 29 days. Days completed before September: January 31 + February 29 + March 31 + April 30 + May 31 + June 30 + July 31 + August 31 = 244. Adding 16 makes 16 September the 260th day of the year. The number of days after 1 January is 260 − 1 = 259, and 259 = 7 × 37 exactly, so there are 0 odd days. 16 September therefore falls on the same weekday as 1 January, namely Monday. Anyone who forgets the leap day gets 258 days, one odd day short, and lands on Sunday; taking February as 28 and also miscounting a 30-day month is what produces the Saturday and Tuesday distractors.

Answer: 3 — Sunday

Days of the week repeat every 7 days, so only the remainder on division by 7 matters. From the 3rd to the 29th is 29 − 3 = 26 days. 26 = 3 × 7 + 5, so the 29th falls 5 weekdays after Tuesday: Wednesday, Thursday, Friday, Saturday, Sunday. The 29th is therefore a Sunday. A quick check: the 3rd, 10th, 17th and 24th are all Tuesdays, and 29 is five days past the 24th — Sunday again. Option 4 (Tuesday) is the trap for anyone who assumes 26 is a multiple of 7, and option 1 (Saturday) comes from counting 4 days instead of 5.

Answer: 1 — Friday

The day before yesterday is two days back from today, so today = Monday + 2 = Wednesday. The day after tomorrow is two days forward from today, so it is Wednesday + 2 = Friday. In short, the day after tomorrow is always four days after the day before yesterday. Option 3 (Sunday) is the trap for counting backwards instead of forwards.

Answer: 2 — Wednesday

Count odd days up to the date. Take 2001 complete years plus 2 days of January 2002. 1600 years give 0 odd days and 400 years give 0 odd days, so 2000 years contribute 0. The single remaining ordinary year (2001) contributes 1 odd day. January 2002 contributes 2 days. Total odd days = 0 + 1 + 2 = 3, and counting 0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday. Cross-check the other way: 1 January 2000 was a Saturday, 2000 was a leap year (366 days = 2 odd days) so 1 January 2001 was a Monday, and 2001 was ordinary (1 odd day) so 1 January 2002 was a Tuesday — making 2 January 2002 a Wednesday. Tuesday (option 4) is the trap because it is the day 1 January fell on.

Answer: 4 — Monday

December has 31 days, so from 3 December 2021 to 3 January 2022 is exactly 31 days. 31 ÷ 7 leaves a remainder of 3, so the day advances by 3 from Friday. Friday + 1 = Saturday, + 2 = Sunday, + 3 = Monday. Sunday (option 1) is the trap for anyone who takes the remainder as 2 by counting 30 days instead of 31.

Answer: 2 — Friday

Days of the week repeat every 7 days, so only the remainder on division by 7 matters (the odd days). 96 ÷ 7 = 13 remainder 5, since 7 × 13 = 91 and 96 − 91 = 5. So the answer is 5 days after Sunday: Monday, Tuesday, Wednesday, Thursday, Friday. Counting 96 as 13 full weeks and mistakenly taking 6 odd days gives Saturday, the trap in option 1.

Answer: 1 — Tuesday

Anchor on the stated day and step forward one day at a time. Day  ·  Which Day before yesterday  ·  Friday Yesterday  ·  Saturday Today  ·  Sunday Tomorrow  ·  Monday Day after tomorrow  ·  Tuesday The day after tomorrow is 4 days after Friday: Friday + 4 = Tuesday. Option 2 (Sunday) is the trap — that is today, not the day after tomorrow.

Answer: 2 — Wednesday

Anchor on 1 January 2000, a Saturday. 2000 is a leap year (366 days = 2 odd days), so 1 Jan 2001 was Monday; 2001 is ordinary (1 odd day), so 1 Jan 2002 was Tuesday. From 1 Jan 2002 to 1 May 2002: Jan 31 + Feb 28 + Mar 31 + Apr 30 = 120 days, and 120 = 17×7 + 1, i.e. 1 odd day. Tuesday + 1 = Wednesday. Note 2002 is not a leap year, so February contributes 28, not 29 — using 29 gives Thursday (option 4), the trap.

Answer: 2 — Saturday

Weekdays repeat every 7 days, so only the remainder matters: 10 ÷ 7 leaves 3. Going back 3 days from Tuesday gives Monday, Sunday, Saturday — so the day was Saturday. The trap is to count 10 back one day at a time and stop early at Sunday, or to treat 10 days ago as 7 days ago and answer Tuesday.

Answer: 3 — Friday

Rule: an ordinary year moves a fixed date forward by 1 weekday and a leap year by 2, so count odd days as (number of years) + (number of 29 Februaries crossed). From 29 July 2010 to 29 July 2022 is 12 years. The 29 Februaries falling inside that window are 2012, 2016 and 2020 — three of them. Odd days = 12 + 3 = 15, and 15 ÷ 7 leaves a remainder of 1. Thursday + 1 day = Friday. The usual slip is to count 2024 as well, or to forget the leap days and answer Tuesday.

Answer: 3 — Friday

Count the days from 18 July to 20 August 2021. July has 31 days, so 31 − 18 = 13 days take you to 31 July, and 20 more take you to 20 August: 13 + 20 = 33 days. Odd days = 33 ÷ 7 = 4 weeks and 5 days remaining, so the answer is 5 days past Sunday: Monday, Tuesday, Wednesday, Thursday, Friday. 20 August 2021 was a Friday. Thursday is the trap for anyone who counts 32 days (forgetting that 31 July itself is day 13), and Sunday for anyone who takes 35 days.

Answer: 1 — Saturday

The day of the week shifts forward by the number of odd days in the year that separates the two dates. The year in between is 2021, which is not divisible by 4, so it is an ordinary year of 365 days. 365 ÷ 7 leaves a remainder of 1, that is one odd day. So 1 January 2022 falls one weekday after 1 January 2021: Friday + 1 = Saturday. Option 4 (Sunday) is what you get if you wrongly treat 2021 as a leap year and add two days.

Answer: 3 — Sunday

Step 1 — jump whole years. From 13 April 2002 to 13 April 2014 is 12 years containing the leap days of 2004, 2008 and 2012, so odd days = 12 + 3 = 15, and 15 ÷ 7 leaves 1. Saturday + 1 = Sunday, so 13 April 2014 was a Sunday. Step 2 — walk back to 9 March 2014. From 9 March to 13 April is 22 (rest of March) + 13 = 35 days, which is exactly 5 weeks, so the day does not change. Therefore 9 March 2014 was also a Sunday.

Answer: 2 — Wednesday

2012 is a leap year, so it has 366 days, but from 1 January to 31 December only 365 days elapse. 365 ÷ 7 leaves a remainder of 1 odd day, so 31 December falls one weekday after 1 January: Tuesday + 1 = Wednesday. The trap is option 4 (Tuesday): a common year begins and ends on the same weekday, but 2012 is a leap year and the extra 29 February pushes the end of the year forward by one day.

Answer: 1 — Saturday

2011 is not divisible by 4, so it is an ordinary year of 365 days. From 1 January to 31 December is 364 days, and 364 = 52 × 7 exactly, so there are no odd days in between. A whole number of weeks later the day repeats, so 31 December 2011 was also a Saturday. The usual slip is to add the single odd day of a 365-day year and answer Sunday (option 3) — but that odd day carries you to 1 January 2012, not to 31 December 2011.

Answer: 4 — Friday

Work in odd days. From 27 October 2011 to 27 October 2021 is 10 years containing three 29-Februaries (2012, 2016, 2020), so 10 × 365 + 3 = 3653 days; 3653 = 521 weeks + 6, so 27 October 2021 was Thursday + 6 = Wednesday. From 27 October 2021 to 23 September 2022 is 331 days (Nov 30 + Dec 31 + Jan 31 + Feb 28 + Mar 31 + Apr 30 + May 31 + Jun 30 + Jul 31 + Aug 31 + Sep 23 + 4 remaining days of October), and 331 = 47 weeks + 2, so the day is Wednesday + 2 = Friday. Checked directly: the gap is 3984 days = 569 weeks + 1, i.e. Thursday + 1 = Friday. The common slip is to treat the second stretch as a full year (+1 odd day) and land on Sunday (option 3).

Answer: 4 — Cannot be determined

Turn each statement into a set of dates. Sadashiv: after January 12 but not later than January 16 gives {13, 14, 15, 16}. Meher: before January 17 but not before January 13 gives {13, 14, 15, 16} as well — the same four dates, so the second statement adds nothing to the first. Four dates survive the overlap, and one of them (13 January) is not even offered, so no single day can be fixed. Options 1, 2 and 3 each name just one of four equally possible dates, so none of them is forced by the information given.

Answer: 4 — Tuesday

1999 is not a leap year (1999 is not divisible by 4), so February 1999 had 28 days. Count forward from 13 February to 1 March: the rest of February is 28 − 13 = 15 days, plus 1 day to reach 1 March, giving 16 days in all. Divide by 7: 16 = 2 × 7 + 2, so 1 March falls 2 weekdays after 13 February. Going back two days from Thursday gives Wednesday, then Tuesday. So 13 February 1999 was a Tuesday. Option 1 (Thursday) is the trap for anyone who assumes the gap is a whole number of weeks; option 3 (Friday) comes from counting the two days forward instead of backward.

Answer: 2 — Thursday

Break the sentence into its two steps. "2 days from today" is one step; "the next day after" that is a second step. So the total is today + 2 + 1 = today + 3 days. Count from today  ·  Day today  ·  Monday +1  ·  Tuesday +2  ·  Wednesday — this is "2 days from today" +3  ·  Thursday — the next day after that So the answer is Thursday. Why the others fail: Wednesday, the answer to the shorter question "what is 2 days from today", is not even offered, which confirms that the extra step is intended; Monday would be today or a full week later; Friday is today + 4, one day too many; Sunday is the day before Monday.

Answer: 2 — 1994

Two years share a calendar only if both have the same leap status and both begin on the same weekday. 2005 is an ordinary year and 1 January 2005 was a Saturday. Count odd days backwards from 2005: an ordinary year shifts the weekday by 1 and a leap year by 2. 2004 (leap) 2, 2003 1, 2002 1, 2001 1, 2000 (leap) 2, 1999 1, 1998 1, 1997 1, 1996 (leap) 2, 1995 1, 1994 1 — running total from 1994 up to 2005 = 1+1+2+1+1+1+2+1+1+1+2 = 14, which is 0 (mod 7). So 1 January 1994 fell on the same weekday as 1 January 2005, and 1994 is also an ordinary year — the calendars match exactly. 1993 began on a Friday and 1999 on a Friday, and 1998 on a Thursday, so none of them repeats in 2005.

Answer: 3 — Tuesday

Work in two steps: first move a whole year, then move within January. Step 1. 2005 is not a leap year (2005 is not divisible by 4), so it has 365 days = 52 weeks + 1 odd day. Moving from 1 January 2005 to 1 January 2006 therefore advances the weekday by 1: Monday + 1 = Tuesday. So 1 January 2006 is a Tuesday. Step 2. From 1 January to 29 January is 28 days, and 28 = 4 × 7, so it is a whole number of weeks and contributes 0 odd days. Hence 29 January 2006 falls on the same weekday as 1 January 2006 — Tuesday. Option 2 (Monday) is the trap for anyone who forgets the single odd day of 2005 and simply carries Monday forward.

Answer: 1 — 2015

Two years share a calendar when (a) both are of the same kind — both ordinary or both leap — and (b) the odd days between them add up to a multiple of 7. An ordinary year contributes 1 odd day, a leap year 2. Count odd days from 2009 up to the year before the repeat: 2009: 1, 2010: 1, 2011: 1, 2012: 2 (leap), 2013: 1, 2014: 1 → total 7 ≡ 0 (mod 7). So 2015 starts on the same weekday as 2009, and both 2009 and 2015 are ordinary years. The calendar repeats in 2015. Option 3 (2016) is a leap year and so cannot match an ordinary year's calendar at all; 2020 is also a leap year; by 2018 the running total of odd days is 10 ≡ 3, not 0.

Answer: 1 — 53

1996 is divisible by 4 and is not a century year, so it is a leap year: 366 days. 366 = 52 × 7 + 2. So every weekday occurs at least 52 times, and two weekdays occur a 53rd time — the two "odd days", which are the first two days of the year. 1 January 1996 = Monday, so 2 January 1996 = Tuesday. Monday and Tuesday are the two extra days, and each occurs 53 times; the other five weekdays occur 52 times. Mondays in 1996 = 53. Option 4 (52) is the count you get if you forget the leap year's second odd day.

Answer: 3 — 2018

A calendar repeats when two conditions hold together: the odd days between the two years add up to a multiple of 7, and both years are of the same kind (both ordinary or both leap). 2007 is an ordinary year, so the answer must also be an ordinary year — which already rules out 2016 (leap). An ordinary year contributes 1 odd day and a leap year 2. Adding from 2007 onwards: Year  ·  Odd days  ·  Running total  ·  Total mod 7 2007  ·  1  ·  1  ·  1 2008  ·  2  ·  3  ·  3 2009  ·  1  ·  4  ·  4 2010  ·  1  ·  5  ·  5 2011  ·  1  ·  6  ·  6 2012  ·  2  ·  8  ·  1 2013  ·  1  ·  9  ·  2 2014  ·  1  ·  10  ·  3 2015  ·  1  ·  11  ·  4 2016  ·  2  ·  13  ·  6 2017  ·  1  ·  14  ·  0 The running total first becomes a multiple of 7 after 2017 is counted, so the calendar repeats in 2018, and 2018 is an ordinary year just like 2007. 2014 (total 3) and 2017 (total 6 at the start of 2017) are simply not clear of the 7.

Answer: 4 — 45 y 6 m 12 d

Subtract date of birth from date of death, column by column. Years: 2018 − 1972 = 46. Months: 3 − 9 is negative, so borrow a year: 46 − 1 = 45 years and 3 + 12 − 9 = 6 months. Days: 24 − 13 = 11. So from 13 September 1972 to 13 September 2017 is 45 years, from 13 September 2017 to 13 March 2018 is 6 months, and 13 March to 24 March is a further 11 days (12 if the day of death is counted as well, which is the count the paper has used). That is 45 y 6 m, which only option 4 carries. Option 3 (49 y) and option 1 (65 y) are far too large, and option 2 (35 y) far too small.

Answer: 4 — 2044

A calendar repeats when the odd days since the reference year total a multiple of 7 and the leap/ordinary character matches. An ordinary year contributes 1 odd day and a leap year 2. 2016 is a leap year, and a leap year's calendar repeats after 28 years provided no non-leap century year (such as 2100) falls in between. 2016 + 28 = 2044, and 2100 is not crossed, so 2044 is the answer. Check the others by counting odd days from 2016: 2016 → 2024: 8 years with 2 leap years = 8 + 2 = 10 odd days ≡ 3 (mod 7). 2016 → 2032: 16 years with 4 leap years = 20 ≡ 6. 2016 → 2040: 24 years with 6 leap years = 30 ≡ 2. 2016 → 2044: 28 years with 7 leap years = 35 ≡ 0. ✓ 2024 is the trap because it is the next leap year, but being a leap year is not enough.

Answer: 1 — 191

Count month by month, remembering that 2021 is not a leap year so February has 28 days. January from the 18th to the 31st, inclusive, is 31 − 18 + 1 = 14 days; February 28; March 31; April 30; May 31; June 30; July up to the 27th is 27. Total = 14 + 28 + 31 + 30 + 31 + 30 + 27 = 191. Option 3 (190) is what you get by taking the plain difference of the two dates and forgetting to add back the starting day.

Answer: 3 — 2027

A year repeats its calendar when the odd days after it total a multiple of 7. A common year gives 1 odd day, a leap year 2. Counting from 2021: 2021 gives 1, 2022 gives 1, 2023 gives 1, 2024 is a leap year and gives 2, 2025 gives 1, 2026 gives 1. The running totals are 1, 2, 3, 5, 6, 7 — the total first reaches 7 (0 mod 7) after 2026, so 2027 repeats the 2021 calendar. 2021 and 2027 both begin on a Friday and both are common years, which is what the repeat needs. Option 2 (2025) is only 4 odd days on.

Answer: 2 — 185 degrees

The hour hand sweeps 360° in 12 hours, i.e. 30° per hour or 0.5° per minute. From midnight to 6:10 a.m. is 6 hours 10 minutes = 370 minutes. Angle turned = 370 × 0.5 = 185°. Equivalently 6 × 30 = 180° for the six full hours, plus 10 × 0.5 = 5° for the extra ten minutes. Option 1 (190 degrees) is the trap of crediting the hour hand with 1° per minute, which is the minute hand's rate divided by six - the minute hand itself turns 6° per minute.

Answer: 4 — West

The minute hand sweeps a full 360° in 60 minutes, so it turns 6° per minute, clockwise. In 45 minutes it turns 45 × 6° = 270° clockwise. Starting at North and turning clockwise: 90° → East, 180° → South, 270° → West. Option 3 (East) is what you get by turning anticlockwise, or by taking 90° instead of 270°.